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

The motive in this article is twofold. First we investigate the geometrical structures of a pseudo-symmetric spacetime (PS)4 with a timelike vector under the condition of conformal flatness. We classify it into two possible types: constant Ricci scalar and closed velocity vector. Then we further study (PS)4 type spacetime solutions of F(R)-gravity theory and demonstrate 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 analyzes are done for the different F(R)-gravity models and the energy conditions are investigated accordingly, supporting the accelerated expansion of the universe. •(PS)4 is classified into two categories: constant Ricci scalar and closed velocity vector.•The effective pressure and energy density in F(R)-gravity under (PS)4 condition is discussed.•Accelerated expansion of the universe is supported.