A power law solution for FRLW Universe with observational constraints

This paper examines a power law solution under $f(R,T)$ gravity for an isotropic and homogeneous universe by considering its functional form as $f(R,T) = R + \xi RT$, where $\xi$ is a positive constant. In $f(R,T)$ gravity, we have built the field equation for homogeneous and isotropic spacetime. The developed model's solution is $a = \alpha t^{\beta}$. We have used the redshift in the range $0 \leq z \leq 1.965$ and obtained the model parameters $\alpha$, $\beta$, $H_0$ by using the Markov Chain Monte Carlo (MCMC) method. The constrained values of the model parameter are as follows: $H_0 = 67.098^{+2.148}_{-1.792}$ km s$^{-1}$ Mpc$^{-1}$, $H_0 = 67.588^{+2.229}_{-2.170}$ km s$^{-1}$ Mpc$^{-1}$, $H_0 = 66.270^{+2.215}_{-2.181}$ km s$^{-1}$ Mpc$^{-1}$, $H_0 = 65.960^{+2.380}_{-1.834}$ km s$^{-1}$ Mpc$^{-1}$, $H_0 = 66.274^{+2.015}_{-1.864}$ km s$^{-1}$ Mpc$^{-1}$ which have been achieved by bounding the model with the Hubble parameter ($H(z)$) dataset, Baryon Acoustic Oscillations (BAO) dataset, Pantheon dataset, joint $H(z)$ + Pantheon dataset and collective $H(z)$ + BAO + Pantheon dataset, respectively. These computed $H_o$ observational values agree well with the outcomes from the Plank collaboration group. Through an analysis of the energy conditions' behaviour on our obtained solution, the model has been examined and analysed. Using the Om diagnostic as the state finder diagnostic tool and the jerk parameter, we have also investigated the model's validity. Our results show that, within a certain range of restrictions, the proposed model agrees with the observed signatures.