Effective equation of state in modified gravity and observational constraints

TL;DR

This paper introduces bulk viscosity into a modified gravity model with an $f(R,T)$ action, deriving an effective equation of state that explains late-time cosmic acceleration and is consistent with observational data.

Contribution

It develops a cosmological model with bulk viscosity in $f(R,T)$ gravity, analyzing its dynamics and observational compatibility, which is a novel approach in modified gravity theories.

Findings

Model explains late-time acceleration effectively.

Consistent with supernova and Hubble data.

Distinguishes from other dark energy models using diagnostic tools.

Abstract

In this article, the bulk viscosity is introduced in a modified gravity model. The gravitational action has a general $f(R,T)$ form, where $R$ and $ T $ are the curvature scalar and the trace of energy momentum tensor respectively. An effective equation of state (EoS) has been investigated in the cosmological evolution with bulk viscosity. In the present scenario, the Hubble parameter which has a scaling relation with the redshift can be obtained generically. The role of deceleration parameter $q$ and equation of state parameter $\omega $ is discussed to explain the late-time accelerating expansion of the universe. The statefinder parameters and Om diagnostic analysis are discussed for our obtained model to distinguish from other dark energy models together with the analysis of energy conditions and velocity of sound for the model. We have also numerically investigated the model by detailed maximum likelihood analysis of $580$ Type Ia supernovae from Union $ 2.1$ compilation datasets and updated $57$ Hubble datasets ($31$ data points from differential age method and $26$ points from BAO and other methods). It is with efforts found that the present model is in good agreement with observations.