Ricci Semi-Symmetric Robertson–Walker Spacetime in f(R)-Gravity - H. Aruna Kumara; Abdul Haseeb; V. Venkatesha; Mohd Bilal (Mathematics)
We investigated the properties of Ricci semi-symmetric Robertson–Walker spacetimes within the framework of <semantics>f(R)</semantics>-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 <semantics>f(R)</semantics>-gravity, deriving expressions for the isotropic pressure p and energy density <semantics>σ</semantics>. To further develop our understanding, we explored various energy conditions to constrain the functional form of <semantics>f(R)</semantics>. We analyzed several models, namely <semantics>f(R)=R−α(1−e−<mstyle scriptlevel="0" displaystyle="true">Rα</mstyle>)</semantics>, <semantics>f(R)=R−βtanhR</semantics>, and <semantics>f(R)=R−log(mR)</semantics>, where <semantics>α</semantics>, <semantics>β</semantics>, 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 <semantics>ω=−1</semantics>. 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.