How a conformally flat (GR)4 impacts Gauss-Bonnet gravity?

TL;DR

This paper explores how conformally flat (GR)4 spacetime influences Gauss-Bonnet gravity, showing it as an Einstein manifold and analyzing energy conditions in modified gravity models consistent with an accelerating universe.

Contribution

It demonstrates that conformally flat (GR)4 spacetime is Einstein and examines its role as a solution in $f(R,G)$-gravity, expressing modifications as a perfect fluid and analyzing energy conditions.

Findings

Weak, null, and dominant energy conditions are satisfied.

Strong energy condition is violated, aligning with an accelerating universe.

Models are consistent with recent observational data.

Abstract

First and foremost, we show that a 4-dimensional conformally flat generalized Ricci recurrent spacetime $(GR)_4$ is an Einstein manifold. We examine such a spacetime as a solution of $f(R, G)$-gravity theory and it is shown that the additional terms from the modification of the gravitational sector can be expressed as a perfect fluid. Several energy conditions are investigated with $f(R, G) = R +\sqrt{G}$ and $f(R, G) = R^2+GlnG$. For both the models, weak, null and dominant energy conditions are satisfied while strong energy condition is violated, which is a good agreement with the recent observational studies which reveals that the current universe is in accelerating phase.