On Spontaneous Compactification in Multidimensional Cosmology

TL;DR

This paper investigates conditions for spontaneous compactification in multidimensional cosmological models with Einstein spaces, scalar fields, and a cosmological constant, finding solutions including wormhole-like and de Sitter generalizations.

Contribution

It derives general conditions for spontaneous compactification in multidimensional Einstein space models with scalar fields and applies these to specific physically relevant cases.

Findings

Existence conditions for solutions with spontaneous compactification.

Discovery of a wormhole-type solution with Euclidean continuation.

Generalization of de Sitter universe to multidimensional context.

Abstract

Mutidimensional cosmological models with $n\left( n\geq 2\right) $ Einstein spaces $M_i\left( i=1,\ldots ,n\right) $ are investigated. The cosmological constant and homogeneous minimally coupled scalar field as a matter sources are considered. The scalar field has a potential of general form depending on the scalar field as well as on the scale factors of $M_i$ . The general condition of existence of the solutions with spontaneous compactification is obtained and applied to physically important cases. Two particular kinds of solutions are found. One of them has a wormhole-type continuation into the Euclidean region. Another one represents the generalization of the de Sitter universe to the multidimensional model under consideration.