Compactification and signature transition in Kaluza-Klein spinor cosmology

TL;DR

This paper explores classical and quantum cosmology in a 5D Kaluza-Klein model with a spinor field, revealing signature transitions and a potential compactification mechanism for extra dimensions.

Contribution

It provides exact solutions for free spinor fields and demonstrates a signature transition mechanism that links to internal-external scale factor behavior.

Findings

Exact solutions for free spinor fields in 5D cosmology

Signature transition from Euclidean to Lorentzian signature

Potential compactification of extra dimension with a~R^{-1}

Abstract

We study the classical and quantum cosmology of a 4+1-dimensional space-time with a non-zero cosmological constant coupled to a self interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor $R(t)$ and an internal scale factor $a(t)$ associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition from a Euclidean to a Lorentzian domain. Such transitions suggest a compactification mechanism for the internal and external scale factors such that $a\sim R^{-1}$ in the Lorentzian region. The corresponding quantum cosmology and the ensuing Wheeler-DeWitt equation have exact solutions in the mini-superspace when the spinor field is free, leading to wavepackets undergoing signature change. The question of stabilization of the extra dimension is also discussed.