diff --git "a/3tE2T4oBgHgl3EQfjgeA/content/tmp_files/load_file.txt" "b/3tE2T4oBgHgl3EQfjgeA/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/3tE2T4oBgHgl3EQfjgeA/content/tmp_files/load_file.txt" @@ -0,0 +1,1488 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf,len=1487 +page_content='Exploring bulk viscous unified scenarios with Gravitational Waves Standard Sirens Weiqiang Yang,1, ∗ Supriya Pan,2, 3, † Eleonora Di Valentino,4, ‡ Celia Escamilla-Rivera,5, § and Andronikos Paliathanasis3, 6, 7, ¶ 1Department of Physics, Liaoning Normal University, Dalian, 116029, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' China 2Department of Mathematics, Presidency University, 86/1 College Street, Kolkata 700073, India 3Institute of Systems Science, Durban University of Technology, PO Box 1334, Durban 4000, Republic of South Africa 4School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, United Kingdom 5Instituto de Ciencias Nucleares, Universidad Nacional Aut´onoma de M´exico, Circuito Exterior C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=', A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 70-543, M´exico D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 04510, M´exico 6Instituto de Ciencias F´ısicas y Matem´aticas, Universidad Austral de Chile, Valdivia 5090000, Chile 7Mathematical Physics and Computational Statistics Research Laboratory, Department of Environment, Ionian University, Zakinthos 29100, Greece We consider the unified bulk viscous scenarios and constrain them using the Cosmic Microwave Background observations from Planck 2018 and the Pantheon sample from Type Ia Supernovae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Then we generate the luminosity distance measurements from O(103) mock Gravitational Wave Standard Sirens (GWSS) events for the proposed Einstein Telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We then combine these mock luminosity distance measurements from the GWSS with the current cosmological probes in order to forecast how the mock GWSS data could be effective in constraining these bulk viscous scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Our results show that a non-zero time dependent bulk viscosity in the universe sector is strongly preferred by the current cosmological probes and will possibly be confirmed at many standard deviations by the future GWSS measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We further mention that the addition of GWSS data can significantly reduce the uncertainties of the key cosmological parameters obtained from the usual cosmological probes employed in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' INTRODUCTION Understanding the nature of dark matter and dark en- ergy has been a challenge for cosmologists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The standard cosmological model, namely, the so-called Λ-Cold Dark Matter (ΛCDM) model representing a mixture of two non-interacting fluids − a positive cosmological constant (Λ > 0) and a cold dark matter component, has un- doubtedly proved its unprecedented success by explain- ing a large span of astronomical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' However, this simplest cosmological scenario has some limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For example, the cosmological constant problem [1] and the coincidence problem [2] have already questioned the ex- isting assumptions in the ΛCDM model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' constant energy density of the vacuum and the non-interacting na- ture between Λ and CDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' These limitations motivated the cosmologists to find alternative cosmological scenar- ios beyond ΛCDM by relaxing the above assumptions, and as a consequence, several new cosmological models were introduced, see [3–12] for a review of various dark energy and modified gravity models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Additionally, the appearance of cosmological tensions at many standard deviations between Planck [13] (assuming ΛCDM in the background) and other cosmological probes, such as dis- tance ladders [14–24] or weak lensing [25–29] and galaxy ∗ d11102004@163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='com † supriya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='maths@presiuniv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='in ‡ e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='divalentino@sheffield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='uk § celia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='escamilla@nucleares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='unam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='mx ¶ anpaliat@phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='uoa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='gr cluster data [30–32] has further weakened the confidence in the ΛCDM cosmological model [33–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Thus, the list of cosmological models aiming to address the cosmolog- ical tensions is increasing in time, see the review arti- cles [38–44] and references therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Given the fact that the origin of dark matter and dark energy is not clearly understood yet, thus, there is no reason to favor any par- ticular cosmological theory over others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As a result, var- ious ways have been proposed to interpret the dynamics of the dark sector in terms of dark matter and dark en- ergy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The simplest assumption is the consideration of independent evolution of these dark fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The general- ization of the above consideration is the assumption of a non-gravitational interaction between these dark sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' On the other hand, a heuristic approach is to consider a unified dark fluid that can explain the dynamics of dark energy and dark matter at cosmological scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The at- tempt to unify the dark sector of the Universe began long back ago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The most simplest unified dark sector mod- els can be constructed in the context of Einstein gravity with the introduction of a generalized equation of state p = F(ρ), where p and ρ are respectively the pressure and energy density of the unified dark sector and F is an an- alytic function of the energy density, ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The well known unified cosmological models, such as the Chaplygin gas model [45] and its successive generalizations, namely, the generalized Chaplygin gas, modified Chaplygin gas, see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [46–57] and some other unified cosmological scenar- ios as well [58–60] belong to this classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' While it is essential to mention that a subset of the unified mod- els has been diagnosed with exponential blowup in the arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='03969v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO] 10 Jan 2023 2 matter power spectrum which is not consistent with the observations [61], however, this does not rule out the pos- sibility of unified models aiming to cover a wide region of the universe evolution because a new kind of unified fluid may avoid such unphysical activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The unified cosmological models can also be developed by considering a relation like p = G(H) where G is an analytic function of H, the Hubble function of the Friedmann-Lemaˆıtre- Robertson-Walker (FLRW) line element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Apparently, theories with p = F(ρ) and p = G(H) seem identical, however, this is only true in spatially flat FLRW uni- verse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For a curved universe, the two approaches are not the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In the present work we are interested to study a partic- ular class of unified models endowed with bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The cosmological fluids allowing bulk viscosity as an ex- tra ingredient can explain the accelerating expansion of the universe, and hence they are also enlisted as possi- ble alternatives to the standard ΛCDM cosmology in the literature [62, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Following an earlier work Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [64] where an evidence of non-zero bulk viscosity was pre- ferred by the current cosmological probes, in the present article, we use the simulated Gravitational Waves Stan- dard Sirens (GWSS) measurements from the Einstein Telescope [65]1 in order to quantify the improvements of the cosmological parameters, if any, from the future GWSS measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As the gravitational waves (GW) have opened a new window for astrophysics and cosmol- ogy, therefore, it will be interesting to investigate the contribution from the simulated GWSS data, once com- bined with the current cosmological probes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' This moti- vated many investigators to use the mock GWSS data matching the expected sensitivity of the Einstein Tele- scope to constrain a class of cosmological models, see for instance, [66–77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In particular,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' the combined analysis of simulated GWSS measurements from Einstein Telescope and the standard cosmological probes has proven to be very effective for a class of cosmological models,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' in the sense that the error bars in the key cosmological param- eters of these cosmological models are significantly re- duced thanks to the mock GWSS dataset [70,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 71,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 74,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 78– 81],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' however,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' in some specific f(R) theories of gravity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' the generated mock GWSS from the Einstein Telescope may not be very much helpful to give stringent constraints on them during its first phase of running [82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Thus, one may expect that the constraining power of the Einstein Telescope may depend on the underlying cosmological model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Aside from the future GWSS measurements from the Einstein Telescope, one can also use the simulated GWSS measurements from other GW observatories, such as, Laser Interferometer Space Antenna (LISA) [83–86] and DECi-heltz Interferometer Gravitational wave Ob- servatory (DECIGO) [87, 88], TianQin [89].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In this ar- ticle, we focus only on the simulated GWSS data from 1 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='einsteintelescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='nl/en/ Einstein Telescope to constrain the bulk viscous unified scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The paper has been organized as follows: in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' II we discuss the gravitational equations for the bulk viscous scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' III describes the observational data that we have considered for the analysis in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' IV presents the observational constraints on the bulk vis- cous models, and mainly we discuss how the inclusion of gravitational waves data from the Einstein Telescope improves the constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Finally, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' V we present the conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' REVISITING THE BULK VISCOUS SCENARIOS: BACKGROUND AND PERTURBATIONS As usual, we consider the homogeneous and isotropic space time described by the Friedmann-Lemaˆıtre- Robertson-Walker (FLRW) line element ds2 = −dt2 + a2(t) � dr2 1 − kr2 + r2 � dθ2 + sin2 θdφ2�� , (1) where a(t) is the expansion scale factor and k denotes the spatial curvature of the universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For k = 0, −1, +1, we have three different geometries of the universe, namely, spatially flat, open and closed, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In this paper we restrict ourselves to the spatially flat scenario where we assume that (i) the gravitational sector is described by the Einstein’s gravity, (ii) the matter sector of the uni- verse consists of the relativistic radiation, non-relativistic baryons and a unified bulk viscous fluid which combines the effects of dark matter and dark energy, (iii) all the fluids are non-interacting with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Within this framework, we can write down the gravitational field equations as follows (in the units where 8πG = 1) H2 = 1 3ρtot, (2) 2 ˙H + 3H2 = − ptot, (3) where an overhead dot indicates the derivative with re- spect to the cosmic time t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' H ≡ ˙a/a is the Hubble ex- pansion rate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' (ρtot, ptot) = (ρr +ρb +ρu, pr +pb +pu) are the total energy density and total pressure of the cosmic components in which (ρr, pr), (ρb, pb), (ρu, pu) are the en- ergy density and pressure of radiation, baryons and the unified fluid, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The conservation equation for each fluid follows the usual law ˙ρi + 3H(1 + wi)ρi = 0, where the subscript i refers to radiation (i = r), baryons (i = b) and the unified fluid (i = u) and wi are the stan- dard barotropic state parameters: wr = pr/ρr = 1/3, wb = pb/ρb = 0 and wu = pu/ρu = (γ − 1), where γ is a constant parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In general for different val- ues of γ, say for instance, γ = 0, we realize a cosmo- logical constant-like fluid endowed with the bulk viscos- ity and similarly γ = 1 results in a dust-like fluid en- dowed with the bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As the nature of the 3 fluid is not clearly understood and as the observational data play an effective role to understand this nature, thus, in order to be more transparent in this direction we consider γ lying in the interval [−3, 3] which includes both exotic (pu/ρu = (γ − 1) < −1/3) and non-exotic (pu/ρu = (γ − 1) > −1/3 ) fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As already mentioned, since the unified fluid has a bulk viscosity, therefore, it en- joys an effective pressure [90]: peff = pu−uν ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='νη(ρu), where uµ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='µ is the expansion scalar of this fluid and η(ρu) > 0 is the coefficient of the bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Thus, in the FLRW background, the effective pressure of the bulk viscous fluid reduces to peff = pu − 3Hη(ρu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' (4) Since there is no unique selection for the bulk viscous coefficient, η(ρu), therefore, we consider a well known choice for it in which the bulk viscous coefficient has a power law evolution of the form [90–92]: η(ρu) = αρm u , (5) where α is a positive constant and m is any real number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Notice that for the case m = 0 we recover the scenario with a constant bulk viscous coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Now, with the consideration of the bulk viscous coefficient in (5), the effective pressure of the unified fluid can be expressed as peff = (γ − 1)ρu − √ 3αρ1/2 tot ρm u , (6) and consequently, one can define the effective equation of state of the viscous dark fluid as weff = peff ρu = (γ − 1) − √ 3αρ1/2 tot ρm−1 u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' (7) The adiabatic sound speed for the viscous fluid is given by c2 a,eff = p′ eff ρ′u = weff + w′ eff 3H(1 + weff).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' (8) where the prime denotes the derivative with respect to the conformal time τ and H is the conformal Hubble pa- rameter, H = aH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Note that depending on the nature of weff, c2 a,eff could be negative, and hence ca,eff could be an imaginary quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' This may invite instabilities in the perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Thus, in order to avoid this possible un- physical situation, we consider the entropy perturbations (non-adiabatic perturbations) in the unified dark fluid following the analysis of generalized dark matter [93].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Now we focus on the evolution of the unified bulk vis- cous fluid at the level of perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In the entropy perturbation mode, the true pressure perturbation comes from the effective pressure given by δpeff = δpu − δη(∇σuσ) − η(δ∇σuσ) = δpu − 3Hδη − η a � θ + h′ 2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' (9) The effective sound speed of viscous dark fluid for the bulk viscous coefficient (5) can be defined as c2 s,eff ≡ �δpeff δρu � rf = c2 s − √ 3αmρ1/2 tot ρm−1 u − αρm−1 u aδu � θ + h′ 2 � , (10) where ’|rf’ denotes the rest frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Following the analysis in [93], the sound speed in the rest frame is assumed to be zero, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' c2 s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The density perturbation and the velocity perturba- tion can also be written as [93] δ′ u = −(1 + weff)(θu + h′ 2 ) + w′ eff 1 + weff δu − 3H(c2 s,eff − c2 a,eff) � δu + 3H(1 + weff)θD k2 � , (11) θ′ u = −H(1 − 3c2 s,eff)θu + c2 s,eff 1 + weff k2δu, (12) Thus, following the evolution at the background and per- turbation level prescribed above, one can now be able to understand the dynamics of the bulk viscous fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In this work we consider two different bulk viscous scenar- ios characterized as follows: the bulk viscous model 1 (labeled as BVF1) where we consider γ = 1, and the bulk viscous model 2 (labeled as BVF2) where we keep γ as a free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The common parameters in both BVF1 and BVF2 are α and m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' STANDARD COSMOLOGICAL PROBES, SIMULATED GWSS DATA, AND METHODOLOGY In this section we describe the cosmological data sets employed to perform the statistical analyses of the present bulk viscous scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Cosmic Microwave Background (CMB): We use the CMB data from the Planck 2018 data re- lease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Precisely, we use the CMB temperature and polarization angular power spectra plikTT- TEEE+lowl+lowE [94, 95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Pantheon sample from Type Ia Supernovae (SNIa) data: Type Ia Supernovae are the first astronomical data that probed the accelerating ex- pansion of the universe and hence indicated the existence of an exotic fluid with negative pressure (dark energy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Here we use the Pantheon compila- tion of the SNIa data comprising 1048 data points spanned in the redshift interval [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='01, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='3] [96].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Gravitational Waves Standard Sirens (GWSS): We take the mock Gravitational Waves Standard Sirens (GWSS) data generated by matching the expected sensitivity of Einstein 4 Telescope in order to understand the constraining power of the future GWSS data from the Einstein Telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The Einstein Telescope is a proposed ground based third-generation (3G) GW detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The telescope will take a triangular shape and its each arm length will be increased to 10 km, compared to 3 km arm length VIRGO and 4 km arm length LIGO [65, 97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Thus, due to such in- creased arm length, the Einstein Telescope will be a potential GW detector by reducing all displace- ment noises [65, 97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' It is expected that after 10 years of operation, Einstein Telescope will detect O(103) GWSS events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Although the detection of O(103) GWSS events is very optimistic while the number of detections could be low in reality [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As argued in [65], the Einstein Telescope will likely to detect 20 − 50 events per year, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 200 − 500 events in 10 years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' However, following the earlier works [66, 67, 70, 71, 74, 77, 79, 81, 82], in this article, we restrict ourselves to the detection of O(103) GWSS events by the Einstein Telescope to constrain the bulk viscous scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For more features of the Einstein Telescope we refer the readers to [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We originally generate the mock GWSS luminosity distance measurements matching the expected sen- sitivity of the Einstein Telescope after 10 years of full operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Specifically we create 1000 triples (zi, dL(zi), σi) where zi is the redshift of a GW source, dL(zi) is the measured luminosity distance at redshift zi and σi is the uncertainty associated with the luminosity distance dL(zi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Let us briefly summarize the procedure of generating the mock GWSS dataset and we refer to Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [70, 71, 81] for more technical details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The initial step for generating the mock GWSS dataset is to identify the expected GW sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We consider the GW events originating from two distinct binary systems, namely, (i) a combination of a Black Hole (BH) and a Neutron Star (NS) merger, identified as BHNS and (ii) the binary neutron star (BNS) merger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Following the mass distributions as described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [81], the ratio of the number of GW events for the BHNS merger versus BNS merger is taken to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='03 as predicted for the Advanced LIGO-VIRGO network [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We then determine the merger rate R(z) of sources and from the merger rate of the sources,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' we determine the redshift distribution of the sources,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' P(z) given by [66,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 67,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 70,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 79,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 81,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 99] P(z) ∝ 4πd2 C(z)R(z) H(z)(1 + z) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' (13) where dC(z) ≡ � z 0 H−1(z′)dz′ is the co-moving dis- tance and for R(z) we take the following piece- wise linear function estimated in [100] (also see [66,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 67,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 70,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 79,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 81,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 101]): R(z) = 1 + 2z for z ≤ 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' R(z) = 3 4(5 − z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' for 1 < z < 5 and R(z) = 0 for z > 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' After having P(z), we sample 1000 values of redshifts from this distribution which represent the redshifts zi of our 1000 mock GWSS data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The next step is to choose a fiducial model because while going from the merger rate to the redshift dis- tributions, a fiducial cosmological model is needed since the expression for P(z) includes both the co- moving distance and expansion rate at redshift z, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' dL(z) and H(z) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' This H(z) cor- responds to the fiducial model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As in this arti- cle we are interested to investigate how the inclu- sion of GWSS data improves the constraints on the BVF models, therefore, we generate two different mock GWSS datasets choosing BVF1 and BVF2 as the fiducial models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We take the fiducial val- ues of the cosmological parameters given by the best fit values of the same cosmological parame- ters of the BVF1 and BVF2 models obtained from the CMB+Pantheon data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Now, for the chosen fiducial model(s), one can now estimate the luminosity distance at the redshift zi using the re- lation dL(zi) = (1 + zi) � zi 0 dz′ H(z′) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' (14) Thus, after having the luminosity distance dL(zi) of the GW source, our last job is now to determine the uncertainty σi associated with this luminosity dis- tance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The determination of the uncertainty σi di- rectly connects to the waveform of GW because the GW amplitude depends on the luminosity distance (also on the so-called chirp mass [66, 67, 79]) and hence one can extract the information about dL(zi) and σi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We refer to Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [66, 67, 70, 79, 81] for the technical details to calculate the uncertainties on the luminosity distance measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The lumi- nosity distance measurement dL(zi) has two kind of uncertainties, one is the instrumental uncertainty σinst i and the other one is the weak lensing uncer- tainty σlens i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The instrumental error can be derived to be σinst i (≃ 2dL(zi)/S where S is the combined signal-to-noise ratio of the Einstein Telescope) us- ing the Fisher matrix approach and assuming that the uncertainty on dL(zi) is not correlated with the uncertainties on the remaining GW parame- ters (see [66, 67, 70, 79, 81]) and the lensing error is σlens i ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='05zidL(zi) [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Thus, the total uncer- tainty due to the instrumental and the weak lensing uncertainties on dL(zi) is σi = � (σinst i )2 + (σlens i )2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Finally, let us note that the combined signal-to- noise ratio of the GW detector is a very crucial quantity in this context since for the Einstein Tele- scope, the combined signal-to-noise ratio should be 5 Parameter Priors (BVF1) Priors (BVF2) Ωbh2 [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='005, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='1] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='005, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='1] τ [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='8] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='8] ns [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5] ln(1010As) [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='4, 4] [2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='4, 4] 100θMC [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5, 10] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5, 10] β [0, 1] [0, 1] m [−2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5] [−2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5] γ − [−3, 3] TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We show the flat priors on all the free parameters associated with the bulk viscous models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' at least 8 for a GW detection [99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Thus, in sum- mary, we generate 1000 GW sources up to redshift z = 2 with S > 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For more technical details we refer the readers to Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [66, 67, 70, 79, 81, 99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' To constrain the BVF scenarios we modify the pub- licly available CosmoMC package [102] which is an excel- lent cosmological code supporting the Planck 2018 like- lihood [95] and it has a convergence diagnostic follow- ing the Gelman-Rubin statistic R − 1 [103].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' It is essen- tial to mention that for both BVF1 and BVF2 scenarios, we have used the dimensionless quantity β = αH0ρm−1 tot,0 where ρtot,0 is the present value of ρtot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We further men- tion here that β = 0 (equivalently, α = 0) implies no vis- cosity and hence the overall picture behaves like a unified cosmic fluid without bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Thus, in summary, the parameter space of BVF1 and BVF2 are as below: PBVF1 ≡ {Ωbh2, 100θMC, τ, ns, ln(1010As), β, m} PBVF2 = {Ωbh2, 100θMC, τ, ns, ln(1010As), β, m, γ} where the description of the free parameters are as fol- lows: Ωbh2 is the baryons density, 100θMC is the ratio of the sound horizon to the angular diameter distance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' τ is the optical depth, ns is the scalar spectral index, As is the amplitude of the initial power spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The flat priors on both cosmological scenarios are shown in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' OBSERVATIONAL CONSTRAINTS: RESULTS AND ANALYSIS In this section we present the constraints on the bulk viscous scenarios considering CMB+Pantheon and CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As we are interested to esti- mate the improvement of the cosmological parameters in presence of the GWSS measurements, and as the com- bined standard cosmological probes offer the most strin- gent constraints on the cosmological parameters, there- fore, the inclusion of GWSS with the combined standard cosmological probes is reasonable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As mentioned earlier, the key common free parameters of BVF1 and BVF2 are β and m, since β ̸= 0 indicates the preference for a non- zero bulk viscosity and m ̸= 0 indicates that the coeffi- cient of the bulk viscosity is not constant in the redshift range considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In the following subsections we discuss the constraints on these two scenarios in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Constraints on the BVF1 scenario In Table II we have presented the constraints on the BVF1 scenario for CMB+Pantheon and CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The latter dataset is aimed to understand the improvement expected from GWSS on the constraints from CMB+Pantheon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 1 we have compared these datasets graphically by showing the one dimensional marginalized distribution of some model pa- rameters and the two dimensional joint contours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As discussed, this scenario has two main key parameters, namely, β, quantifying the existence of bulk viscosity in the cosmic sector, and m, which tells us whether the bulk viscosity will have a dynamical nature (corresponding to m ̸= 0) or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Since for CMB+Pantheon, we find an evidence for a non-zero bulk viscosity in the cosmic sector at many standard deviations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='430+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='017 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='016 at 68% CL, this is further strengthen for CMB+Pantheon+GWSS, where β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='4262+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0079 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0078 at 68% CL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='2 One can clearly see that the inclusion of GWSS to CMB+Pantheon im- proves the error bars on β by a factor of at least 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' This reflects the constraining power of GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' On the other hand, focusing on the parameter m, which quanti- fies the time evolution of the bulk viscosity, we see that m remains non-zero at several standard deviations for CMB+Pantheon, where the 68% CL constraint on m is m = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='557+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='068 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='059, and becomes m = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='519+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='038 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='035 for CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' From the constraints on m, one can clearly see that the uncertainty in m is re- duced by a factor of ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='7 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='8 when the GWSS data are included with the combined dataset CMB+Pantheon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Concerning the Hubble constant, we find that H0 as- sumes slightly higher values compared to the ΛCDM based Planck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Actually, we have H0 = 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='1+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='2 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='1 at 68% CL for CMB+Pantheon, while H0 = 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='30+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='46 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='45 at 68% CL for CMB+Pantheon+GWSS, again improving the uncertainty in H0 by a factor of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' This shows that the effects of GWSS are clearly visible through these param- eters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 1, one can compare the constraints on the model parameters obtained from CMB+Pantheon and CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 2 It is worthwhile to note here that the mean value of β is not significantly changed when the GWSS data are included, because we built the simulated data using the best fit obtained from CMB+Pantheon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 6 Parameters CMB+Pantheon CMB+Pantheon+GWSS Ωbh2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='02232+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00015+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00029 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00015−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00028 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='02253+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00014+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00028 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00014−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00026 100θMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='02780+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00058+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0011 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00055−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0011 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='02808+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00037+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00073 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00038−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00073 τ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0537+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0074+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='016 −0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='85 TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We report the observational constraints on the BVF1 scenario at 68% and 95% CL for CMB+Pantheon and CMB+Pantheon+GWSS datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 64 66 68 70 72 H0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='8 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='7 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='4 m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0228 Ωbh 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='39 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='42 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='48 β 64 66 68 70 72 H0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='4 m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0220 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0228 Ωbh 2 BVF1: CMB+Pantheon BVF1: CMB+Pantheon+GWSS FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For the BVF1 scenario we show the 1-dimensional posterior distribution of some model parameters and the 2- dimensional joint contours of the model parameters at 68% and 95% CL for CMB+Pantheon and CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Finally, through Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 2 we examine how the model af- fects the CMB TT power spectrum for different values of the model parameters, β and m with respect to the standard ΛCDM scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In the upper panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 2 we depict the evolution in the CMB TT power spectrum for different values of β while in the lower panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 2 we depict the evolution in the CMB TT power spectrum for different values of m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' From both the graphs, we no- tice that as long as β or m increases, the model exhibits significant differences in the lower multipoles (ℓ ≤ 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For ℓ ≥ 10, we observe that with the increasing values of β and m, the peaks of the CMB TT power spectrum increase significantly, particularly changing their mutual ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 7 Parameters CMB+Pantheon CMB+Pantheon+GWSS Ωbh2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='02241+0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='91+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='59+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='1 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='60−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='2 TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We report the observational constraints on the BVF2 scenario at 68% and 95% CL for CMB+Pantheon and CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 101 102 103 l 0 1000 2000 3000 4000 5000 6000 7000 l(l + 1)C TT l /(2π)[µK 2] ΛCDM BVF1 : β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='1 BVF1 : β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='3 BVF1 : β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5 101 102 103 l 0 2000 4000 6000 8000 10000 12000 l(l + 1)C TT l /(2π)[µK 2] ΛCDM BVF1 : m = − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5 BVF1 : m = − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5 BVF1 : m = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The CMB CT T l power spectrum versus multipole moment l using the best fits values obtained for the BVF1 model using the join data sets described, with three arbitrary β and m values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Constraints on the BVF2 scenario In Table III we present the constraints on the BVF2 scenario for both CMB+Pantheon and CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' And in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 3, we com- pare the constraints from these datasets explicitly showing the one dimensional marginalized distribution of some model parameters and the two dimensional joint contours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As already discussed, this scenario has three main key parameters, namely, β, which quantifies the existence of bulk viscosity in the cosmic sector, m, which tells us whether the bulk viscosity enjoys a dynamical nature (corresponding to m ̸= 0) or not, and finally, the parameter γ, which indicates the fluid which endows the bulk viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We note that γ = 1 refers to the dust fluid endowing the bulk viscosity in which we are interested in, for which we recover the previous scenario BVF1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For CMB+Pantheon, we find that β ̸= 0 at several standard deviations yielding β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='447 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='022 at 68% CL which gives a clear indication of a non-zero bulk viscosity in the cosmic sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' When the GWSS are added to this combination, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' CMB+Pantheon+GWSS, the conclusion about β does not change significantly (β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='425+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='018 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='016 at 68% CL), indicating that for this scenario GWSS do not provide any additional constrain- ing power on β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Looking at the dynamical nature of the bulk viscosity, we see that for CMB+Pantheon, m re- mains nonzero at more than 2 standard deviations lead- ing to m = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='85+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='30 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='19 at 68% CL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' However, this evi- dence could be further strengthened by the inclusion of the GWSS data, that we forecast to be m = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='683+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='099 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='089 at 68% CL for CMB+Pantheon+GWSS, improving the error bars up to a factor of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Finally, focusing on the pa- rameter γ which directly connects with the nature of the cosmic fluid endowing the bulk viscosity, we can see that it is consistent with 1, which corresponds to a dust-like fluid, within 2 standard deviations for CMB+Pantheon (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='9970+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0015 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0024 at 68% CL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Also for this param- eter, the addition of the GWSS further improves the constraining power of a factor larger than 3 to 4, that we forecast to be γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='99757+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00049 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00058 at 68% CL for CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Therefore, with respect to the BVF1 case, where the inclusion of the forecasted GWSS was able to improve both β and m, in this BVF2 scenario, the improvement of the constraining power is displayed only on m and γ but does not affect anymore β signifi- 8 60 64 68 72 H0 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='6 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='8 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='4 m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='993 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='999 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='005 γ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='022 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0228 Ωbh 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='44 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='48 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='52 β 60 64 68 72 H0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='4 m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='993 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='999 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='005 γ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0220 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='0228 Ωbh 2 BVF2: CMB+Pantheon BVF2: CMB+Pantheon+GWSS FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For the BVF2 scenario we show the 1-dimensional posterior distributions of some model parameters and the 2- dimensional joint contours of the model parameters at 68% and 95% CL for CMB+Pantheon and CMB+Pantheon+GWSS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' cantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Furthermore, we find that for this scenario, the Hub- ble constant attains a very low value for CMB+Pantheon compared to Planck’s estimation within the ΛCDM paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We also note that H0 is correlated to all three free parameters of this scenario, namely, β, m and γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' With β and γ, H0 is positively correlated while with m, it has a strong anti-correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' For CMB+Pantheon, H0 = 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='2+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='7 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='6 km/s/Mpc at 68% CL and after the in- clusion of GWSS it becomes H0 = 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='91+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='59 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='60 km/s/Mpc at 68% CL, reducing the uncertainty in H0 by a factor of ∼ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Finally, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 4, we examine the CMB TT power spectrum for this bulk viscous scenario BVF2 consider- ing different values of the free parameter γ with respect to the standard ΛCDM scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As γ lies in the region [−3, 3] and the nature of the cosmic fluid characterized by its equation of state pu = (γ−1)ρu depends on the sign of γ, therefore, we have considered two separate plots, one where γ is non-negative (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' γ ≥ 0) and another plot where γ allows both positive and negative values includ- ing γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' From both the panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 4, we clearly see that any deviation from γ = 1 makes significant changes in the amplitude of the CMB TT power spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In particular, we see that the peaks of the CMB TT spec- trum significantly increases and shift towards higher mul- tipoles for any value different from γ = 1 at small scales, as well as the Integrated Sachs Wolfe (ISW) plateau at large scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' As γ = 1 indicates a cosmological constant- like fluid endowed with the bulk viscosity, therefore, for γ = 1, we replicate an equivalent behaviour of the ΛCDM scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' CONCLUSIONS Although the ΛCDM cosmological model is extremely successful in describing a large span of astronomical ob- servations, it cannot explain several theoretical and ob- servational issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' This motivated the scientific com- munity to construct a variety of cosmological proposals and testing them with the available astronomical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Among these cosmological models, in this article, we fo- cus on the unified cosmological models allowing bulk vis- 9 101 102 103 l 0 2000 4000 6000 8000 10000 12000 l(l + 1)C TT l /(2π)[µK 2] ΛCDM BVF2 : γ = − 1 BVF2 : γ = 0 BVF2 : γ = 1 101 102 103 l 0 2000 4000 6000 8000 10000 12000 l(l + 1)C TT l /(2π)[µK 2] ΛCDM BVF2 : γ = 0 BVF2 : γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='5 BVF2 : γ = 1 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The CMB CT T l power spectrum versus multipole moment l using the best fits values obtained for each BVF2 models with three γ values, respectively using the join data sets described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' cosity in the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' However, since these models do not recover the ΛCDM scenario as a special case, our only ability in distinguishing them, once the GWSS data will be available, will rely only on a Bayesian model com- parison for a better fit of the cosmological observations, as done in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' The unified cosmological scenar- ios endowed with bulk viscosity are appealing from two different perspectives: the first one is the concept of a unified picture of dark matter and dark energy, and the second is the inclusion of bulk viscosity into that unified picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Effectively, the unified bulk viscous scenario is a generalized cosmic picture combining two distinct cos- mological directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' According to a recent paper on the unified bulk viscous scenarios [64], current cosmological probes prefer a non-zero dynamical bulk viscosity in the dark sector at many standard deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' So, in light of the current cosmological probes, unified bulk viscous cos- mological scenarios are attractive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In this line of thought, what about the future of such unified bulk viscous sce- narios?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In this article we have focused on it with an answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [64], in this work we have explored these scenarios with the GWSS aiming to understand how the future distance measurements from GWSS may improve the constraints on such scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In order to proceed toward this confrontation, we have generated O(103) mock GWSS luminosity distance measurements matching the expected sensitivity of the Einstein Tele- scope and added these mock data to the current cosmo- logical probes, namely CMB from Planck 2018 release3 and SNIa Pantheon sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' We find that the inclusion of GWSS luminosity distance measurements together with the current cosmological probes makes the possible fu- ture evidence for new physics stronger, by reducing the uncertainty in the parameters in a significant way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' This is a potential behaviour of the GWSS luminosity distance measurements since this makes the parameter much de- terministic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Overall for both BVF1 and BVF2 scenar- ios, we find a very strong preference of a non-zero time dependent bulk viscous coefficient (alternatively, the vis- cous nature of the unified dark fluid) at many standard deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' In conclusion, in the present paper we demonstrate that future GWSS distance measurements from the Ein- stein Telescope might be powerful to extract more infor- mation about the physics of the dark sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Therefore, based on the present results, we feel that it might just be a matter of time before we convincingly detect the viscosity in the dark sector, if any.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' ACKNOWLEDGMENTS The authors thank the referee for some important com- ments which helped us to improve the article consider- ably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' WY was supported by the National Natural Science Foundation of China under Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 12175096 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 11705079, and Liaoning Revitalization Talents Program under Grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' XLYC1907098.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' SP acknowledges the financial support from the Department of Science and Technology (DST), Govt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' of India, under the Scheme “Fund for Improvement of S&T Infrastructure (FIST)” [File No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' SR/FST/MS-I/2019/41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' EDV is supported by a Royal Society Dorothy Hodgkin Research Fellow- ship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' CE-R is supported by the Royal Astronomical So- ciety as FRAS 10147 and by PAPIIT UNAM Project TA100122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' This article/publication is based upon work from COST Action CA21136 Addressing observational tensions in cosmology with systematics and fundamen- tal physics (CosmoVerse) supported by COST (European Cooperation in Science and Technology).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' AP was sup- ported in part by the National Research Foundation of South Africa (Grant Number 131604).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Also AP thanks the support of Vicerrector´ıa de Investigaci´on y Desarrollo Tecnol´ogico (Vridt) at Universidad Cat´olica del Norte 3 We mention that in the earlier work [64], CMB data from Planck 2015 were used to 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Wang, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Yang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' D 97, 103005 (2018), arXiv:1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00952 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [70] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Mota, JCAP 07, 037 (2019), arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='08286 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [72] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' D 100, 123539 (2019), arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='02327 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [74] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Pan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} 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+page_content=' 497, 879 (2020), arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='02180 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [75] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Mitra, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Mifsud, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Mota, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Parkin- son, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 502, 5563 (2021), arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='00189 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [76] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Escamilla-Rivera and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Quevedo, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 38, 115009 (2021), arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='08784 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [77] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Pan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' He, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Qi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Cao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Liu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Wang, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' 911, 135 (2021), arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='05212 [astro- ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [78] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Zhang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Zhang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' D 99, 063510 (2019), arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='08379 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO].' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Zhang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' B 782, 87 (2018), arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='04720 [astro- ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [80] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Di Valentino, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Holz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Melchiorri, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Renzi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' D 98, 083523 (2018), arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='07463 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [81] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Du, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Xu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Pan, and D.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Matos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Calv˜ao, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Waga, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' D 103, 104059 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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' D 66, 103511 (2002), arXiv:astro-ph/0205436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' [103] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Gelman and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Rubin, Statist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE2T4oBgHgl3EQfjgeA/content/2301.03969v1.pdf'} +page_content=' Sci.' metadata={'source': 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