Energy Conditions in Non-minimally Coupled $f(R,T)$ Gravity

TL;DR

This paper investigates energy conditions in a linear $f(R,T)$ gravity model with a perfect fluid, demonstrating its compatibility with accelerated cosmic expansion and analyzing the implications of energy condition violations.

Contribution

It introduces a linear $f(R,T)$ gravity model constrained by energy conditions and cosmological data, highlighting its potential to explain accelerated expansion.

Findings

Model supports accelerated expansion consistent with observations.

DEC and WEC are satisfied, validating the model.

SEC violation indicates accelerated universe expansion.

Abstract

In today's scenario, going beyond Einstein's theory of gravity leads us to some more complete and modified gravity theories. One of them is the $f(R,T)$ gravity in which $ R $ is the Ricci scalar, and $ T $ is the trace of the energy-momentum tensor. Using a well-motivated linear $f(R,T)$ gravity model with a single parameter, we studied the strong energy condition (SEC), the weak energy condition (WEC), the null energy condition (NEC), and the dominant energy condition (DEC) under the simplest non-minimal matter geometry coupling with a perfect fluid distribution. The model parameter is constrained by energy conditions and a single parameter proposed equation of state (EoS), resulting in the compatibility of the $f(R,T)$ models with the accelerated expansion of the universe. It is seen that the EoS parameter illustrate the quintessence phase in a dominated accelerated phase, pinpoint to the cosmological constant yields as a prediction the phantom era. Also, the present values of the cosmological constant and the acceleration of the universe are used to check the viability of our linear $f(R,T)$ model of gravity. It is observed that the positive behavior of DEC and WEC indicates the validation of the model. In contrast, SEC is violating the condition resulting in the accelerated expansion of the universe.