Holographic F(Q,T) Gravity with Lambert Solution

In this work, we study a model of holographic dark energy using FLRW cosmology in the context of modified gravity. An extension of the symmetric teleparallel gravity is obtained by considering the gravitational action L is given by an arbitrary function f of the non-metricity Q, where the nonmetricity Q is responsible for the gravitational interaction, and of the trace of the matter-energy-momentum tensor T, so that \(L=f(Q,T)\) $L=f(Q,T)$ . We expand on the features of the derived cosmological model in view of the relation between cosmic time and redshift as \(t(z)=\frac{kt_{0}}{b}f(z)\) $t(z)=\frac{k{t}_0}{b}f(z)$ where \(f(z)=W\left[ \frac{b}{k}e^{\frac{b-ln(1+z)}{k}} \right] \) $f(z)=W\left[\frac{b}{k},e^{\frac{b-ln(1+z)}{k}}\right]$ and W denotes the Lambert function, and discuss the evolution trajectories of the equation of state parameter and deceleration parameters in the evolving universe using a special then a generalized version of the model.