Ricci Semi-Symmetric Robertson–Walker Spacetime in f ( R )-Gravity

We investigated the properties of Ricci semi-symmetric Robertson–Walker spacetimes within the framework of f ( R ) -gravity theory. Initially, we established that Ricci semi-symmetric Robertson–Walker spacetimes are locally isometric to either Minkowski or de Sitter spacetimes. We then focused on the 4-dimensional formulation of these spacetimes in f ( R ) -gravity, deriving expressions for the isotropic pressure p and energy density σ . To further develop our understanding, we explored various energy conditions to constrain the functional form of f ( R ) . We analyzed several models, namely f ( R ) = R − α ( 1 − e − R α ) , f ( R ) = R − β tanh R , and f ( R ) = R − log ( m R ) , where α , β , and m are constants. Our findings suggest that the equations of state parameters for these models are compatible with the universe’s accelerating expansion, indicating an equation of state parameter ω = − 1 . Moreover, while these models satisfy the null, weak, and dominant energy conditions reflective of the observed accelerated expansion, our analysis reveals that they violate the strong energy condition.