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.

Automated summary

In this paper, a cosmological toy model is presented, where a non-minimally coupled varying speed of light and varying gravitational constant are considered. The model is extended using the Eisenhart-Duval lifting method, and the system's evolution is depicted as a geometrical flow associated with the lifted metric. The Dirac-Wheeler-DeWitt equation is derived and its solution describes the emergence of early universe-antiuniverse pairs with differing conserved quantities analogous to spin.