Generalized gravity theory with curvature, torsion and nonmetricity

In this article, the generalized gravity theory with the curvature, torsion and nonmetricy was studied. For the FRW spacetime case, in particular, the Lagrangian, Hamilatonian and gravitational equations are obtained. The particular case $F(R,T)=alpha R+beta T+mu Q+ u{cal T}$ is investigated in detail. In quantum case, the corresponding Wheeler-DeWitt equation is obtained. Finally, some gravity theories with the curvature, torsion and nonmetricity are presented.