Viscous Fluid Models of Cosmic Acceleration in FRW Spacetime Using MCMC Constraints

TL;DR

This work investigates a bulk viscous modified Chaplygin gas in a flat FRW universe, deriving analytical solutions for both viscous and non-viscous limits and examining how viscosity alters density evolution, the Hubble rate, and the deceleration parameter. The authors constrain three model cases using Markov Chain Monte Carlo against Hubble parameter data and Pantheon SNIa measurements, revealing parameter regions that closely track the expansion history while remaining consistent with $\Lambda$CDM trends. A key finding is that bulk viscosity suppresses structure-formation oscillations and drives late-time acceleration without a cosmological constant, with the effective sound speed indicating overall dynamical stability. The results highlight that the viscosity parameter $\xi$ and equation-of-state parameter $\gamma$ are tightly constrained by current data, and the methodology paves the way for exploring extensions to non-flat geometries and time-dependent viscosity in the context of alternative gravity theories.

Abstract

This study combines theoretical advancements with observational limitations to investigate the cosmological implications of a bulk viscous modified Chaplygin gas (MCG) in a Friedmann--Robertson--Walker (FRW) in (3+1) dimensional spacetime framework. We provide analytical solutions for both viscous and non-viscous cases, pointing out variations in the energy density evolution, the Hubble parameter dynamics, and the deceleration parameter transitions. Bulk viscosity suppresses oscillations in structure creation, a well-known drawback of Chaplygin gas models in larger dimensions, as shown by a thorough perturbation analysis. Using the bulk viscosity coefficient and Hubble expansion parameter, which are incorporated by the total pressure and the appropriate pressure and by using energy momentum conservation law determined time time-dependent density. With the help of three conditions ($ξ= 0$, $ξ\neq0$, and we neglect both bulk viscosity and presence of Chaplygin gas, i.e $A=0$ and $ξ=0$) created three different models as the Hubble parameter is a function of redshift $z$. By applying the MCMC method to these models, we have gone through observational analysis by using the Hubble and BAO datasets.

Figures (18)

• Figure 1: Model(1) Confidence contours and marginalized posterior distributions for the parameters $H_0$, $A$, $d$ and $\gamma$ obtained from the Hubble (OHD) dataset.
• Figure 2: Model(1) Hubble data Error graph compare with $\Lambda\ CDM$ model
• Figure 3: Model(1) MCMC-based posterior distributions for parameters $H_0$, $A$, $d$ and $\gamma$ using the Pantheon Type Ia Supernova dataset.
• Figure 4: Model(1) Pantheon data Error graph compare with $\Lambda\ CDM$ model
• Figure 5: Model(1) Combined parameter constraints from joint Hubble (OHD) and Pantheon Type Ia Supernova datasets.