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)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L=f(Q,T)$$\end{document}. We expand on the features of the derived cosmological model in view of the relation between cosmic time and redshift as t(z)=kt0bf(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t(z)=\frac{kt_{0}}{b}f(z)$$\end{document} where f(z)=Wbkeb-ln(1+z)k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(z)=W\left[ \frac{b}{k}e<^>{\frac{b-ln(1+z)}{k}} \right] $$\end{document} 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.