A conformally flat generalized Ricci recurrent spacetime in F(R)-gravity

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 R in R 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.

Automated summary

This study examines a conformally flat generalized Ricci recurrent perfect fluid spacetime as a solution of modified F(R)-gravity theory, showing the characteristics of various energy conditions. The results indicate that both cases studied in the context of current observational studies of accelerated expansion of the Universe satisfy the energy conditions, while violating the strong energy condition.