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The $f(Q,T)$ cosmological model has emerged as a promising framework forunderstanding various aspects of cosmic evolution. In this study, we focused onobtaining the constraints of the free parameters in the non-linear form ofnon-metricity in $f(Q,T)$ gravity using the $Hubble$, $Pantheon$, and $BAO$datasets. To determine the best-fit values for the model parameters and theequation of state (EoS) parameter, we employed an MCMC analysis. By examiningthe error bar plots, we observed that both the model curve and the $\Lambda$CDMcurve successfully passed through the range obtained from the datasets.Additionally, we studied the state finder diagnostics and energy conditions togain insights into the properties of the model. Furthermore, we conducted ananalysis using the $Om(z)$ diagnostic, which provides a null test for thevalidity of the $\Lambda$CDM model.

Constrained cosmological model in $f(Q,T)$ gravity with non-linear non-metricity