Reconstruction of $f(R,T)$ gravity model via the Raychaudhuri equation

TL;DR

This paper derives an analytical $f(R,T)$ gravity model using the Raychaudhuri equation, analyzing its viability and stability during matter and dark energy eras, and finds the strong energy condition is violated, consistent with current universe acceleration.

Contribution

It introduces a new analytical $f(R,T)$ gravity model based on geometrical methods, exploring its stability and energy conditions across cosmic eras.

Findings

Strong energy condition is not satisfied, aligning with accelerated universe observations.

Model remains stable under the considered conditions.

Viability of the $f(R,T)$ model is demonstrated for different cosmic eras.

Abstract

In this work, we investigate for an analytical solution under modified gravity theory, specifically the $f(R,T)$ gravity for two different eras, i.e., matter and dark energy dominated accelerating universe from completely geometrical and mathematical point of view with the help of the Raychaudhuri equation. To construct $f(R,T)$ gravity model, we consider the functional form of $f(R,T)$ as the sum of two independent functions of the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$, respectively. Under the consideration of this type of power law expansion of the Universe we have studied the viability, stability and all the energy conditions. We note that the strong energy condition is not satisfied in our model, which is obvious for the present scenario of the Universe.