The simplest invariant cosmological model in $f(R,T)$ gravity

In the present work, we search the simplest invariant cosmological model in $f(R,T)$ gravity by considering it's functional form $f(R,T) = R + \xi R T$ with $\xi$ being positive constant. We have constructed the Einstein's field equation in $f(R,T)$ gravity for in-homogeneous space time. The general solution of the constructed model is obtained as $a = f(x)g(t)$ and $g(t)$ is expressed as $g(t) = \alpha t^{\beta}$ with $\alpha$ and $\beta$ being the free parameters. The values of $\alpha$ and $\beta$ are obtained by using Markov Chain Monte Carlo (MCMC) method to constraining the model under consideration with observational $H(z)$ data. Some physical and kinematic properties of the model are also discussed.