Running vacuum cosmology with bulk viscous matter

TL;DR

This paper investigates late-time cosmic acceleration by combining running vacuum energy with bulk viscous matter, deriving analytical solutions, fitting observational data, and analyzing the universe's thermodynamic and dynamical stability.

Contribution

It introduces a model with variable vacuum energy and bulk viscosity proportional to Hubble parameter, providing analytical solutions and observational constraints.

Findings

Estimated universe age as 14 Gyr, slightly higher than ΛCDM.

Bulk viscosity coefficient is much lower than in previous models.

Model predicts a transition redshift of 0.73 and a stable, thermodynamically consistent universe.

Abstract

We study the late acceleration of the universe by incorporating bulk viscous matter with the running vacuum. The vacuum energy density varies as the squares of the Hubble parameter ($\rho_{\Lambda}\propto H^2$), and the coefficient of bulk viscosity of matter is proportional to the velocity of expansion ($\xi \propto H$). We obtained an analytical solution to the Friedmann equations and estimated the model parameters using the combined data set SN1a+CMB+BAO+OHD. We have evaluated the universe's age as 14 Gyr, which is slightly higher than the age-predicted by the $\Lambda$CDM model. However, it is an improved result compared to the age-predicted by a class of bulk viscous matter-dominated models. Interestingly, we have obtained the coefficient of bulk viscosity of the matter component as $1.316\times 10^5$ kg $\textnormal m^{-1}$ $\textnormal s^{-1}$ which is one to two orders of magnitude less than the value predicted by most of the bulk viscous matter-dominated models and it falls in the range of highly viscous materials found on the earth. The Hubble parameter is a decreasing function of the scale factor, and it attains a constant value in the far future that corresponds to an end deSitter phase of evolution. The deceleration parameter shows a transition from matter-dominated decelerated phase to vacuum energy-dominated accelerating phase, and the transition redshift is obtained as $z_T = 0.73$. The statefinder analysis distinguishes our model from the $\Lambda$CDM model at present, and the $r-s$ trajectory reveals the quintessence behaviour of the vacuum energy. The phase space analysis shows that the universe is evolving towards a mechanically stable state in the far future. The entropy evolution satisfies the generalised second law of thermodynamics, and the entropy is maximised in the far future evolution.