On Signature Transition and Compactification in Kaluza-Klein Cosmology

Details On Signature Transition and Compactification in Kaluza-Klein Cosmology On Signature Transition and Compactification in Kaluza-Klein Cosmology

1999-05-03

arxiv.org/abs/gr-qc/9905008v1

Class.Quant.Grav. 16 (1999) 1565-1575

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 3 figures

Scientific paper

10.1088/0264-9381/16/5/307

We consider an empty (4+1) dimensional Kaluza-Klein universe with a negative cosmological constant and a Robertson-Walker type metric. It is shown that the solutions to Einstein field equations have degenerate metric and exhibit transitioins from a Euclidean to a Lorentzian domain. We then suggest a mechanism, based on signature transition which leads to compactification of the internal space in the Lorentzian region as $a \sim |\Lambda|^{1/2}$. With the assumption of a very small value for the cosmological constant we find that the size of the universe $R$ and the internal scale factor $a$ would be related according to $Ra\sim 1$ in the Lorentzian region. The corresponding Wheeler-DeWitt equation has exact solution in the mini-superspace giving rise to a quantum state which peaks in the vicinity of the classical solutions undergoing signature transition.

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