Isolation of the true degree of freedom and normalizable wave functions for the general type V cosmology

The quantization of the most general Type V geometry (with all six scale factors as well as the shift vector present) is considered. The information carried by the linear constraints is used to reduce the Wheeler–DeWitt equation (arising from a valid Hamiltonian found earlier), which initially included six variables, to a final PDE in three variables, getting rid of three redundant variables (gauge degrees of freedom). The full space of solutions to this equation is presented. In trying to interpret these wave functions, we are led through further consideration of the action of the automorphism group on the configuration space, to a final reduction to the one and only true degree of freedom, i.e. the only independent curvature invariant of the slice t=constant. Thus, a normalizable wave function in terms of the true degree of freedom is obtained.