$f(Q,T)$ gravity models with observational constraints

Abstract: The paper presents late time cosmology in $f(Q,T)$ gravity where the dark energy is purely geometric in nature. We start by employing a well motivated $f(Q,T)$ gravity model, $f(Q,T)=mQ^{n}+bT$ where $m,n$ and $b$ are model parameters. Additionally we also assume the universe to be dominated by pressure-less matter which yields a power law type scale factor of the form $% a(t)=c_{2}(At+c_{1})^{\frac{1}{A}}$, where $A=\dfrac{3(8\pi +b)}{n(16\pi +3b)% }$ and $c_{1}$ & $c_{2}$ are just integration constants. To investigate the cosmological viability of the model, constraints on the model parameters were imposed from the updated 57 points of Hubble data sets and 580 points of union 2.1 compilation supernovae data sets. We have thoroughly investigated the nature of geometrical dark energy mimicked by the parametrization of $f(Q,T)=mQ^{n}+bT$ with the assistance of statefinder diagnostic in ${s,r}$ and ${q,r}$ planes and also performed the $Om$ -diagnostic analysis. The present analysis makes it clear-cut that $f(Q,T)$ gravity can be promising in addressing the current cosmic acceleration and therefore a suitable alternative to the dark energy problem. Further studies in other cosmological areas are therefore encouraging to further investigate the viability of $f(Q,T)$ gravity.