Role of viscous fluid in FLRW model with observational constraints

Abstract

In this study, we investigate the role of bulk viscosity in the evolution of a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe dominated by dust. By parameterizing the bulk viscosity as \(\tilde{p}= -3(l + m (H'(t) + H^2) + n H^2) H\), we derived the modified Einstein field equations and reformulate them in terms of the redshift z. Using the Hubble datasets with 46 data points and Pantheon+ compilation with 1701 supernova measurements, we estimated the model parameters (\(H_0\), l, m, n) through \(\chi ^{2}\) minimization and refined them using Markov chain Monte Carlo (MCMC) simulations. Our analysis reveals a transition redshift \(z_t = 0.585\), marking the universe’s shift from decelerated to accelerated expansion, and a current deceleration parameter \(q_0 =- 0.705\) consistent with the \(\Lambda\)CDM model. The current age of the universe obtained from our model was \(t_{0}\) = 14.5734 Gyrs. Additionally, we estimate the present Hubble constant, \(H_0\), to be 68 km/s/Mpc based on the Hubble datasets and approximately 73 km/s/Mpc using the Pantheon+ datasets. The best-fit cosmological parameters indicate a recent transition to accelerated expansion at \(z_{t} \approx 0.55\), a present-day deceleration parameter \(q_{0} \approx -0.55\), a Hubble constant in the range \(67\; to- 74 kms^{-1} Mpc^{-1}\), and a cosmic age \(t_{0} \approx 13.7\) Gyr, consistent with current observational constraints. This disparity highlights the ongoing Hubble tension-a discrepancy between locally measured values of \(H_0\) (e.g., via supernovae) and values inferred from the early universe (e.g., CMB observations). Our findings are consistent with the larger trend of greater \(H_0\) values from late-universe observations compared with early-universe predictions, highlighting the need for more research into the underlying physical or systematic sources of this tension. We further evaluate the evolution of the cosmological parameters, including the equation of state parameter \(\omega (z)\), energy density \(\rho (z)\) and pressure p(z). Statefinder diagnostics (r, s) demonstrate the versatility of the model, capturing its deviation from and convergence toward \(\Lambda\)CDM at specific epochs. This study emphasizes the importance of bulk viscosity in explaining the universe’s accelerated expansion and provides a strong framework for assessing various cosmological theories.