F Darabi and H R Sepangi 1999 Class. Quantum Grav. 16 1565 doi:10.1088/0264-9381/16/5/307
On signature transition and compactification in Kaluza-Klein cosmology
F Darabi and H R Sepangi
Show affiliationsWe 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 the Einstein field equations have a degenerate metric and exhibit transitions 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 ~ |
|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 ~ 1 in the Lorentzian region. The corresponding Wheeler-DeWitt equation has an exact solution in the mini-superspace giving rise to a quantum state which peaks in the vicinity of the classical solutions undergoing signature transition.
- PACS
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04.50.-h Higher-dimensional gravity and other theories of gravity
- MSC
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83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
- Subjects
- Dates
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Issue 5 (May 1999)
Received 13 August 1998, in final form 21 December 1998
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On signature transition and compactification in Kaluza-Klein cosmology
F Darabi and H R Sepangi 1999 Class. Quantum Grav. 16 1565
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