Signature change induces compactification

TL;DR

This paper demonstrates that classical signature change in a cosmological model can lead to a novel compactification mechanism, resulting in a stable internal space and a Lorentzian four-dimensional universe with inflation.

Contribution

It introduces a new compactification mechanism driven by classical signature change in a FRW model with specific spatial topology.

Findings

Internal scale factor of order Λ^{-1/2}

Solutions are stable against small perturbations

Effective 4D spacetime exhibits Lorentzian signature and exponential inflation

Abstract

It is shown -- using a FRW model with ${\bf S}^3 \times {\bf S}^6$ 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 ${\bf S}^6$, it is shown that the effective four-dimensional space-time metric has Lorentzian signature, undergoes exponential inflation in ${\bf S}^3$ and is unique. Speculations concerning relations to quantum cosmology and conceivable modifications are added.