Multi-dimensional classical and quantum cosmology: Exact solutions, signature transition and stabilization

TL;DR

This paper presents exact classical and quantum solutions for a higher-dimensional cosmological model, demonstrating signature transition from Euclidean to Lorentzian space and internal space stabilization, with quantum wavefunctions peaking around classical paths.

Contribution

It provides new exact solutions in multi-dimensional cosmology that incorporate signature transition and internal space stabilization, advancing understanding of quantum cosmological models.

Findings

Signature transition occurs in exact solutions.

Quantum wavefunctions peak around classical trajectories.

Internal space stabilization is achieved through signature change.

Abstract

We study the classical and quantum cosmology of a $(4+d)$-dimensional spacetime minimally coupled to a scalar field and present exact solutions for the resulting field equations for the case where the universe is spatially flat. These solutions exhibit signature transition from a Euclidean to a Lorentzian domain and lead to stabilization of the internal space, in contrast to the solutions which do not undergo signature transition. The corresponding quantum cosmology is described by the Wheeler-DeWitt equation which has exact solutions in the mini-superspace, resulting in wavefunctions peaking around the classical paths. Such solutions admit parametrizations corresponding to metric solutions of the field equations that admit signature transition.