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

TL;DR

This paper investigates weakly Ricci symmetric spacetimes in $F(R)$-gravity, demonstrating they behave as perfect fluids with specific energy conditions, and analyzes models supporting accelerated cosmic expansion.

Contribution

It provides new insights into energy conditions for $(WRS)_4$ spacetimes in $F(R)$-gravity and examines specific models consistent with accelerated universe expansion.

Findings

Energy conditions constrain $F(R)$ models.

Models support $oxed{ ext{accelerating universe}}$ with $oxed{ ext{EoS parameter } extstyle oxed{ ext{-1}}}$.

Null, weak, and dominant energy conditions are satisfied; strong energy condition is violated.

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.