Energy conditions for a $(WRS{)}_4$ spacetime in $F(R)$-gravity

Abstract

The objective of the present paper is to study 4-dimensional weakly Ricci symmetric spacetimes $(WRS{)}_4$ with non-zero constant Ricci scalar. We prove that such a $(WRS{)}_4$ satisfying $F(R)$-gravity field equations represents a perfect fluid with vanishing vorticity. Some energy conditions are studied under the current setting to constrain the functional form of $F(R)$. We examine a couple of popular toy models in $F(R)$-gravity, $F(R)=e^{\alpha R}$ where $\alpha$ is constant and $F(R)=R-\beta \tanh (R)$, $\beta$ is a constant. We also find that the equation of state parameter (EoS) in both models supports the universe's accelerating behavior, i.e., $\omega =-1$. According to the recently suggested observations of accelerated expansion, both cases define that the null, weak, and dominant energy conditions justify their requirements while the strong energy conditions violate them.

arXiv commentEPJP published version

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• Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity
• On Pseudo $B$-symmetric spacetimes and $f(\mathcal{R})$ gravity
• Characterization of generalized quasi-Einstein manifolds and modified gravity