Constraining $\boldsymbol{f(R,T)}$ Gravity from the Dark Energy Density Parameter $\boldsymbol{\Omega}_{\boldsymbol{\Lambda}}$

Abstract

$f(R,T)$ gravity is a widely used extended theory of gravity introduced by Harko et al., which is a straightforward generalization of $f(R)$ gravity. The action in this extended theory of gravity incorporates well-motivated functional forms of the Ricci scalar $R$ and the trace of the energy momentum tensor $T$. The present manuscript aims at constraining the most widely used $f(R,T)$ gravity model of the form $f(R+2\lambda T)$ to understand its coherency and applicability in cosmology. We communicate here a novel method to find a lower bound on the model parameter $\lambda\gtrsim-1.9\times 10^{-8}$ through the equation relating the cosmological constant ($\Lambda$) and the critical density of the universe ($\rho_{\textrm{cr}}$).