Viscous FRW Cosmology in Modified Gravity

TL;DR

This paper explores a modified gravity model with a scalar curvature power law, analyzing cosmic fluid dynamics with viscosity and revealing conditions for cosmological evolution and potential future singularities.

Contribution

It introduces a generalized gravity framework with scalar curvature power , including viscous effects, and derives conditions for consistent cosmological solutions.

Findings

Bulk viscosity proportional to (2 - 1) of scalar expansion.

Consistency requires specific viscosity dependence, linking to future singularity scenarios.

Model satisfies energy-momentum conservation for general .

Abstract

We discuss a modified form of gravity implying that the action contains a power \alpha of the scalar curvature. Coupling with the cosmic fluid is assumed. As equation of state for the fluid, we take the simplest version where the pressure is proportional to the density. Based upon a natural ansatz for the time variation of the scale factor, we show that the equations of motion are satisfied for general \alpha. Also the condition of conservation of energy and momentum is satisfied. Moreover, we investigate the case where the fluid is allowed to possess a bulk viscosity, and find the noteworthy fact that consistency of the formalism requires the bulk viscosity to be proportional to the power (2\alpha -1) of the scalar expansion. In Einstein's gravity, where \alpha=1, this means that the bulk viscosity is proportional to the scalar expansion. This mathematical result is of physical interest; as discussed recently by the present authors, there exists in principle a viscosity-driven transition of the fluid from the quintessence region into the phantom region, implying a future Big Rip singularity.