A complete study of conformally flat pseudo-symmetric spacetimes in the theory of F(R)-gravity

TL;DR

This paper explores conformally flat pseudo-symmetric spacetimes within F(R)-gravity, classifying their types, analyzing their physical properties, and supporting accelerated cosmic expansion through observational and energy condition studies.

Contribution

It provides a comprehensive classification of pseudo-symmetric spacetimes in F(R)-gravity and links their geometric properties to cosmological phenomena.

Findings

Classification of pseudo-symmetric spacetimes into two types

Relations between energy density, pressure, and geometry

Support for accelerated universe expansion

Abstract

We investigate the geometrical and physical structures of a pseudo-symmetric spacetime $(PS)_4$ with timelike vector under the condition of conformal flatness. We classify it into two possible types: constant Ricci scalar and closed velocity vector. We further study this spacetime as a solution of $F(R)$-gravity theory and show that the pressure and energy density of the effective cosmological perfect fluid separately possess certain typical relations with the geometry and the gravity sector of the theory. Based on this result, some observational and cosmological analyses are done for the $F(R)$-gravity model and the energy conditions are investigated, supporting the accelerated expansion of the universe.