Eisenhart--Duval lift for minisuperspace quantum cosmology

Abstract

We study covariant equations in quantum cosmology of an extended minisuperspace obtained by the Eisenhart--Duval lift. We find that a Dirac-type equation is naturally introduced in the extended minisuperspace. Explicit forms of the fundamental solutions are yielded for specific models. The possible further development in this direction is also discussed.

19 pages, no figure. Final version

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• Spinor wave function of the Universe in non-minimally coupled varying constants cosmologies
• Linearization of Newton's second law
• Fermionic quantum cosmology as a framework for resolving type IV singularities
• Cosmogenesis as symmetry transformation
• Time-covariant Schrödinger equation and invariant decay probability: The $\Lambda$-Kantowski-Sachs universe