This work analyzes a power law solution under [Formula: see text] gravity for an isotropic and homogeneous universe. To construct [Formula: see text] gravity model, we consider the functional form of [Formula: see text] as the sum of two independent functions of the Ricci scalar R and the trace of the energy–momentum tensor T, i.e. [Formula: see text], with [Formula: see text] being a positive constant where we study the cosmological model under the following two cases: (i) [Formula: see text] and (ii) [Formula: see text]. In the framework of [Formula: see text] gravity with homogeneous and isotropic spacetime, the constructed model yields several features on application of the scale factor [Formula: see text]. We employed the Markov Chain Monte Carlo (MCMC) approach to get model parameters [Formula: see text], [Formula: see text] and [Formula: see text] over a redshift range of [Formula: see text]. The model parameter’s restricted values are listed below: [Formula: see text] km s[Formula: see text][Formula: see text]Mpc[Formula: see text], [Formula: see text][Formula: see text]km[Formula: see text]s[Formula: see text] Mpc[Formula: see text], [Formula: see text][Formula: see text]km[Formula: see text]s[Formula: see text] Mpc[Formula: see text], [Formula: see text][Formula: see text]km[Formula: see text]s[Formula: see text][Formula: see text]Mpc[Formula: see text], [Formula: see text][Formula: see text]km[Formula: see text]s[Formula: see text][Formula: see text]Mpc[Formula: see text]. The model was constrained using the Hubble parameter ([Formula: see text]) dataset, Baryon Acoustic Oscillations (BAO) dataset, Pantheon dataset, joint [Formula: see text] + Pantheon dataset and collective [Formula: see text] + BAO + Pantheon dataset. The results from the Planck collaboration group are consistent with these calculated Ho observed values. In order to study and analyze the model, we first look at how the energy circumstances affected our power law assumption. The validity of the model has also been evaluated using the [Formula: see text] diagnostic and the jerk parameter, which are state finding diagnostic tools. We find that the model under investigation agrees with the observed fingerprints within a certain range of constraints.
