Cosmic evolution in f(Q,T) gravity with observational constraints: A comparative analysis with ΛCDM

In this investigation, we explore the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model within the framework of the $f(Q,T)$ modified gravitation theory. This theory was recently introduced to account for the late cosmic acceleration of our Universe. To address the modified field equations derived from the $f(Q,T)=\alpha Q+\beta Q^2+kT$ form of the $f(Q,T)$ function, we assume a redshift-dependent deceleration parameter. Our goal is to impose observational constraints on the model parameters, ensuring its viability and alignment with the observable Universe's characteristics. The observational constraints are derived from a diverse dataset, encompassing Cosmic Chronometers (CC), type Ia supernovae (SNIa), Baryon Acoustic Oscillation (BAO), Gamma Ray Burst (GRB), and Quasar (Q) measurements. Employing the Markov Chain Monte Carlo (MCMC) technique with the CC + BAO + SNIa + GRB + Q dataset, we conduct simulations to obtain constraints on the model parameters. In the subsequent segments of the study, we delve into the evolution of the constrained model from the past to the present. We utilize metrics such as deceleration and jerk parameters, statefinder pairs, the $O_m$ diagnostic, and various physical parameters of the model. This detailed analysis allows us to scrutinize the transition of the model from a decelerating phase in the past to the late accelerating phase, comparing its evolution with established dark energy models. To assess the model's goodness of fit, we employ statistical criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), P-value, and L-statistic. Remarkably, these criteria consistently indicate that the ΛCDM model is slightly favored by the observational data compared to the proposed cosmological model.