The present analysis examines the parametrized Hubble parameter (HP) to address the field equations (FEs) relevant to cosmic scenarios within the confines of \(f\left( {R,T} \right)\) gravity. We assessed the model’s predictive capability using Bayesian Markov Chain Monte Carlo (MCMC) techniques, analyzing 58 \(H\left( z \right)\) data points and updated SN Ia (Pantheon+) samples that embrace 1,701 points, in addition to 8 baryon acoustic oscillation (BAO) values derived from late-time cosmic observations. This analysis aimed to establish restrictions on the model’s parameters. The results from the behavior of the cosmographic parameters suggest that the Universe is grappling with seamless expansion, shifting from earlier stages of deceleration to an accelerating trend in both the near and distant future. We utilized statefinder diagnostics followed by \(Om\left( z \right)\) diagnostics for assessing the phase evaluations. Energy conditions (ECs) further substantiate the dominance of energy density in the rapidly expanding Universe, while the squared sound speed \(\left( {v_{s}^{2} } \right)\) component demonstrates the model’s stability at present times. We also calculated the universe’s age. Our findings are consistent with observational data, suggesting that the proposed parametrization may effectively elucidate the rapidly expanding Universe by incorporating the evolution of energy components.
