Cosmological perfect-fluids in f(R) gravity

TL;DR

This paper demonstrates that certain generalized Robertson-Walker space-times in f(R) gravity models inherently exhibit perfect fluid stress-energy tensors, extending to conformally flat cases in quadratic gravity.

Contribution

It proves that divergence-free conformal curvature in GRW space-times leads to perfect fluids in f(R) gravity, including quadratic gravity, highlighting geometric conditions for perfect fluids.

Findings

GRW space-times with divergence-free conformal curvature have perfect fluid stress-energy tensors.

Conformally flat GRW space-times are perfect fluids in f(R) and quadratic gravity.

Results apply to higher-dimensional cosmological models.

Abstract

We show that an n-dimensional generalized Robertson-Walker (GRW) space-time with divergence-free conformal curvature tensor exhibits a perfect fluid stress-energy tensor for any f(R) gravity model. Furthermore we prove that a conformally flat GRW space-time is still a perfect fluid in both f(R) and quadratic gravity where other curvature invariants are considered.