Spinor wave function of the Universe in non-minimally coupled varying constants cosmologies

In this paper, we introduce a non-minimally coupled varying speed of light and varying gravitational constant cosmological toy model. Using the Eisenhart–Duval lifting method, we extend the original minisuperspace of the model and depict the evolution of the system in the presence of the potential term as a geometrical flow associated with the lifted metric. We write the Dirac–Wheeler–DeWitt equation, which solution is a spinor wave function of the Universe. Then we find the solution of the Dirac–Wheeler–DeWitt equation, which describes the emergence of two early universe–antiuniverse pairs that differ with the conserved quantity, which is an analog of the spin.