A Conformally Flat Generalized Ricci Recurrent Spacetime in F(R)-Gravity

TL;DR

This paper investigates a specific conformally flat spacetime in F(R)-gravity, showing conditions for Ricci recurrence, analyzing energy conditions with popular models, and relating findings to cosmic acceleration observations.

Contribution

It demonstrates that Robertson-Walker spacetime is generalized Ricci recurrent iff Ricci symmetric, and examines energy conditions in specific F(R) models with cosmological implications.

Findings

Robertson-Walker spacetime is Ricci recurrent iff Ricci symmetric.

Energy conditions are satisfied for certain F(R) models.

Strong energy condition is violated, consistent with accelerated universe expansion.

Abstract

In the present paper we study a conformally flat generalized Ricci recurrent perfect fluid spacetime with constant Ricci scalar as a solution of modified $F(R)$-gravity theory. We show that a Robertson-Walker spacetime is generalized Ricci Recurrent if and only if it is Ricci symmetric. The perfect fluid type matter is shown to have EoS $\omega=-1$. Some energy conditions are analyzed with couple of popular toy models of $F(R)$-gravity, like $F(R)= R+\alpha R^m $ where $\alpha, m$ are constants and $ F(R)=R+\beta RlnR $ where $\beta $ is constant. In harmony with the recent observational studies of accelerated expansion of the universe, both cases exhibit that the null, weak, and dominant energy conditions fulfill their requirements whereas the strong energy condition is violated.