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−Rα), f(R)=R−βtanhR, and f(R)=R−log(mR), 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.