Power-law solution for homogeneous and isotropic universe in $f(R,T)$ gravity

In the present work, we search the simplest cosmological model in $f(R,T)$ gravity by considering its functional form $f(R,T)=R+\xi RT$ with $\xi$ being positive constant. We have constructed the Einstein’s field equation in $f(R,T)$ gravity for homogeneous and isotropic space time. The explicit solution of the constructed model is obtained by considering the scale factor as $a=\alpha t^{\beta }$ with $\alpha$ and $\beta$ being 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.