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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 $f(R,T) = R + ξR T$ with $ξ$ 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 $a = αt^β$ with $α$ and $β$ being free parameters. The values of $α$ and $β$ 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.