Bianchi-I classical and quantum spinor cosmology with signature change

TL;DR

This paper explores classical and quantum Bianchi I cosmology with a Dirac spinor, revealing a signature change mechanism from Euclidean to Lorentzian regions influenced by a negative cosmological constant.

Contribution

It introduces a detailed analysis of signature change in spinor cosmology and provides explicit quantum wave functions linking classical solutions to quantum states.

Findings

Signature change occurs with negative cosmological constant.

Quantum wave functions relate to classical signature-changing solutions.

Quantum states impose a quantization condition on the spinor mass.

Abstract

We study the classical and quantum evolution of a universe in which the matter source is a massive Dirac spinor field and the universe is described by a Bianchi type I metric. We focus attention on those classical solutions that admit a degenerate metric in which the scale factors have smooth behavior in transition from a Euclidean to a Lorentzian domain and show that this transition happens when the cosmological constant, $\Lambda$, is negative. The resulting quantum cosmology and the corresponding Wheeler-DeWitt equation are also studied and closed form expressions for the wave functions of the universe is presented. We have shown that there is a close relationship between the quantum states and signature changing classical solutions, suggesting a mechanism for creation of a Lorentzian universe from a Euclidean region by a continuous change of signature. The quantum solutions also represent a quantization rule for the mass of the spinor field.