The Wheeler-DeWitt equation of $f(R,L_m)$ gravity in minisuperspace

Abstract: In this paper we present the Wheeler-DeWitt equation of $f(R,L_m)$ gravity in flat FRW universe, which is the first step of the study of quantum $f(R,L_m)$ cosmology. In the minisuperspace spanned by the FRW scale factor $a$ and the Ricci scalar $R$, we explicitly examine and verify the equivalence of the reduced action. We then canonical quantize the $f(R,L_m)$ model and derive the corresponding Wheeler-DeWitt equation.