Classical and quantum spinor cosmology with signature change

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.

13 pages, 4 figures

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• Spinors, Inflation, and Non-Singular Cyclic Cosmologies
• Currents and the Energy-Momentum Tensor in Classical Field Theory: A fresh look at an Old Problem
• Nonlinear spinor field in cosmology
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• Variational equations on mixed Riemannian-Lorentzian metrics
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• Time reparameterization in Bianchi type I spinor cosmology
• f(T) Quantum Cosmology
• An Exact Fermionic Chern-Simons-Kodama State in Quantum Gravity
• Compactification and signature transition in Kaluza-Klein spinor cosmology
• Quantum cosmology in teleparallel gravity with a boundary term