Classical and quantum spinor cosmology with signature change

Details Classical and quantum spinor cosmology with signature change Classical and quantum spinor cosmology with signature change

2005-02-16

arxiv.org/abs/gr-qc/0502076v2

JCAP 0505 (2005) 006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 4 figures

Scientific paper

10.1088/1475-7516/2005/05/006

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.

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