Modified gravity in a viscous and non-isotropic background

TL;DR

This paper investigates the evolution of specific $f(R)$ gravity models within a viscous, anisotropic universe, demonstrating their stability, late-time behavior akin to quintessence, and compliance with energy conditions.

Contribution

It introduces viable power law $f(R)$ models in a viscous Bianchi type-I universe and analyzes their stability and late-time cosmological behavior.

Findings

Power law $f(R)$ models are stable with suitable parameters.

Models behave like quintessence at late times.

Shear viscosity tends to zero as time progresses.

Abstract

We study the dynamical evolution of an $f(R)$ model of gravity in a viscous and anisotropic background which is given by a Bianchi type-I model of the Universe. We find viable forms of $f(R)$ gravity in which one is exactly the Einsteinian model of gravity with a cosmological constant and other two are power law $f(R)$ models. We show that these two power law models are stable with a suitable choice of parameters. We also examine three potentials which exhibit the potential effect of $f(R)$ models in the context of scalar tensor theory. By solving different aspects of the model and finding the physical quantities in the Jordan frame, we show that the equation of state parameter satisfy the dominant energy condition. At last we show that the two power law $f(R)$ models behave like quintessence model at late times and also the shear coefficient viscosity tends to zero at late times.