Exploring the Viability of $f(Q, T)$ Gravity: Constraining Parameters with Cosmological Observations

In this paper, we explore the model of $f(Q,T)$ gravity, an extension of symmetric teleparallel gravity where the nonmetricity scalar $Q$ is non-minimally coupled to the trace of the energy-momentum tensor $T$. To ensure general covariance and theoretical consistency, we adopt the covariant formulation of $f(Q, T)$ gravity, which allows a coordinate-independent treatment of the field equations and facilitates the correct identification of effective energy-momentum components. The model is developed as an alternative to the standard $\Lambda$CDM cosmological model and is analyzed using Cosmic Chronometer and Pantheon$^+$ supernovae datasets. Through Markov Chain Monte Carlo analysis, we constrain the model parameters $\alpha$, $\beta$, and $H_0$, and compare the performance of the model with $\Lambda$CDM by evaluating statistical measures such as chi-square, Akaike information criterion (AIC), and Bayesian information criterion (BIC). The results show that the $f(Q, T)$ model effectively mimics $\Lambda$CDM while offering an alternative explanation based on modified gravity. We also examine cosmographic parameters like the deceleration parameter, confirming the transition of the Universe from deceleration to acceleration, and the violation of the strong energy condition, which aligns with observed late-time cosmic acceleration. Additionally, the model provides age estimates for the Universe that are consistent with current observations.