Late time phantom characteristic of the model in f(R,T) gravity with quadratic curvature term

We propose a novel cosmological framework within the $f(R,T)$ type modified gravity theory, incorporating a non-minimally coupled with the higher order of the Ricci scalar ($R$) as well as the trace of the energy–momentum tensor ($T$). Therefore, our well-motivated chosen $f(R,T)$ expression is $R+R^m+2\lambda T^n$, where $\lambda$, $m$, and $n$ are arbitrary constants. Taking a constant jerk parameter ($j$), we derive expressions for the deceleration parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift $z$. We constrained our model with the recent Observational Hubble Dataset (OHD), $Pantheon$, and $Pantheon$ + OHD datasets by using the analysis of Markov Chain Monte Carlo (MCMC). Our model shows early deceleration followed by late-time acceleration, with the transition occurring in the redshift range $1.10\le z_{tr}\le 1.15$. Our findings suggest that this higher-order model of $f(R,T)$ gravity theory can efficiently provide a dark energy model for addressing the current scenario of cosmic acceleration.