Friedmann model with viscous cosmology in modified gravity theory

C. P. Singh; Pankaj Kumar

doi:10.1140/epjc/s10052-014-3070-5

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2014) 74: 3070
https://doi.org/10.1140/epjc/s10052-014-3070-5

Regular Article - Theoretical Physics

Friedmann model with viscous cosmology in modified gravity theory

C. P. Singh^* and Pankaj Kumar

Department of Applied Mathematics, Delhi Technological University (Formerly Delhi College of Engineering), Bawana Road, Delhi, 110 042, India

^* e-mail: cpsphd@rediffmail.com

Received: 19 June 2014
Accepted: 9 September 2014
Published online: 1 October 2014

Abstract

In this paper, we introduce the bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function $$f(R,T)$$ , where $$R$$ and $$T$$ denote the curvature scalar and the trace of the energy–momentum tensor, respectively, within the framework of a flat Friedmann–Robertson–Walker model. As an equation of state for a prefect fluid, we take $p=(\gamma -1)\rho$ , where $0 \le \gamma \le 2$ and a viscous term as a bulk viscosity due to the isotropic model, of the form $\zeta =\zeta _{0}+\zeta _{1}H$ , where $\zeta _{0}$ and $\zeta _{1}$ are constants, and $$H$$ is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non-viscous and viscous fluids, respectively, by assuming a simplest particular model of the form of $$f(R,T) = R+2f(T)$$ , where $f(T)=\alpha T$ ( $\alpha$ is a constant). A big-rip singularity is also observed for $\gamma <0$ at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of $\alpha$ to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits a transition from a decelerated phase to an accelerated phase under certain constraints of $\zeta _0$ and $\zeta _1$ . We compare the viscous models with the non-viscous one through the graph plotted between the scale factor and cosmic time and find that the bulk viscosity plays a major role in the expansion of the universe. A similar graph is plotted for the deceleration parameter with non-viscous and viscous fluids and we find a transition from decelerated to accelerated phase with some form of bulk viscosity.