Eur. Phys. J. Plus (2021) 136: 218
https://doi.org/10.1140/epjp/s13360-021-01216-2

Regular Article

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

¹ Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Jalan Sungai Long, 43000, Cheras, Malaysia
² Institute of Mathematical Sciences, University of Malaya, 50603, Kuala Lumpur, Malaysia
³ Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, 500078, Hyderabad, India

^d pksahoo@hyderabad.bits-pilani.ac.in

Received: 21 October 2020
Accepted: 10 February 2021
Published online: 16 February 2021

Abstract

The objective of the present paper is to study four-dimensional weakly Ricci symmetric spacetimes ${(WRS)}_4$ with nonzero 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.