Viscous Modified Gravity on a RS Brane Embedded in AdS5

TL;DR

This paper investigates how a viscous modified gravity fluid on a Randall-Sundrum II brane embedded in AdS5 can lead to a Big Rip singularity, extending known 4D results to a 5D brane-world context.

Contribution

It extends the analysis of viscous modified gravity effects from 4D to a 5D brane-world model, identifying conditions for Big Rip singularity in this setting.

Findings

Bulk viscosity can drive the universe into the phantom region.

The Big Rip occurs for lpha > 1/2, similar to 4D models.

Scale factors on the brane and in the bulk are proportional.

Abstract

We consider a modified gravity fluid on a Randall-Sundrum II brane situated at y=0, the action containing a power \alpha of the scalar curvature. As is known from 4D spatially flat modified gravity, the presence of a bulk viscosity may drive the cosmic fluid into the phantom region (w < -1) and thereafter inevitably into the Big Rip singularity, even it is initially nonviscous and lies in the quintessence region (w > -1). The condition for this to occur is that the bulk viscosity contains the power (2\alpha-1) of the scalar expansion. We combine this with the 5D RS II model, and find that the Big Rip, occurring for \alpha > 1/2, carries over to the metric for the bulk metric, |y|>0. Actually, the scale factors on the brane and in the bulk become simply proportional to each other.