Signature change induces compactification

Abstract

It is shown -- using a FRW model with ${\mathbf{S}}^3\times {\mathbf{S}}^6$ as spatial sections and a positive cosmological constant -- that classical signature change implies a new compactification mechanism. The internal scale factor is of the order ${\Lambda }^{-1/2}$, and the solutions are stable against small perturbatons. In the case of compactified ${\mathbf{S}}^6$, it is shown that the effective four-dimensional space-time metric has Lorentzian signature, undergoes exponential inflation in ${\mathbf{S}}^3$ and is unique. Speculations concerning relations to quantum cosmology and conceivable modifications are added.

31 pages, LaTeX, 4 Figures are available on request as hard copies. Some clarifications are included concerning the particular model of signature change considered; misprints corrected and some references added

References in corpus (5)

• Failure of Standard Conservation Laws at a Classical Change of Signature
• Hamiltonian quantization of General Relativity with the change of signature
• On Cosmological Isotropy, Quantum Cosmology and the Weyl Curvature Hypothesis
• Black holes, cosmological singularities and change of signature
• Actions for signature change

Cited by in corpus (11)

• Avoiding singularities in Lorentzian-Euclidean black holes: the role of atemporality
• Signature Change on the Brane
• On Signature Transition and Compactification in Kaluza-Klein Cosmology
• Actions for signature change
• Signature change from Schutz's canonical quantum cosmology and its classical analogue
• Classical and quantum spinor cosmology with signature change
• Complex lapse, complex action and path integrals
• Quantum creation and inflationary universes: a critical appraisal
• On metric-connection compatibility and the signature change of space-time
• Compactification and signature transition in Kaluza-Klein spinor cosmology
• Signature transition and compactification