Classical and quantum spinor cosmology with signature change

TL;DR

This paper explores classical and quantum cosmology involving Dirac spinor fields, focusing on signature change phenomena and deriving wavefunctions of the universe, revealing conditions for signature transitions and energy quantization.

Contribution

It provides a comprehensive analysis of Einstein-Dirac systems with signature change, including exact solutions and quantum wavefunctions for free and self-interacting spinor fields.

Findings

Signature transitions occur for negative cosmological constant with self-interacting fields.

Signature changing solutions are absent for free massless spinor fields.

Quantum wavefunctions suggest a quantization rule for the universe's energy.

Abstract

We study the classical and quantum cosmology of a universe in which the matter source is a massive Dirac spinor field and consider cases where such fields are either free or self-interacting. We focus attention on the spatially flat Robertson-Walker cosmology and classify the solutions of the Einstein-Dirac system in the case of zero, negative and positive cosmological constant $\Lambda$. For $\Lambda<0$, these solutions exhibit signature transitions from a Euclidean to a Lorentzian domain. In the case of massless spinor fields it is found that signature changing solutions do not exist when the field is free while in the case of a self-interacting spinor field such solutions may exist. The resulting quantum cosmology and the corresponding Wheeler-DeWitt equation are also studied for both free and self interacting spinor fields and closed form expressions for the wavefunction of the universe are presented. These solutions suggest a quantization rule for the energy.