Observationally constrained accelerating cosmological model with higher power of non-metricity and squared trace

Abstract: In this paper, a cosmological model of the Universe is presented in $f(Q,T)$ gravity and the parameters are constrained by cosmological data sets. Initially, a generalised form of $f(Q,T)$ model is used as $f(Q,T)=-\lambda_{1} Q^{m}-\lambda_{2} T^2$, where $\lambda_{1}$, $\lambda_{2}$ and $m$ are model parameters. With some algebraic manipulation, the Hubble parameter is obtained in terms of redshift. Then, using MCMC analysis, the model parameters are constrained using the most current Hubble and Pantheon$^{+}$ data. The model parameters are also verified through the BAO data set. The model shows an early deceleration transitioning to an accelerating phase of the Universe. The $Om(z)$ diagnostics indicate a positive slope, favouring the model to be in a phantom field dominated phase.