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

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.

10 pages, 6 figures: Revised version submitted to Fortschritte der Physik - Progress of Physics