Compactification and signature transition in Kaluza-Klein spinor cosmology
May, 2006Citations per year
Abstract: (arXiv)
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 and an internal scale factor 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 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.Note:
- 12 pages, 1 figure, to appear in Annals of Physics
- 04.20.-q
- 04.60.-m
- 04.50.+h
- Kaluza-Klein model
- dimension: 5
- cosmological constant
- spinor: massive
- signature: transition
- quantum cosmology
- Wheeler-DeWitt equation
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