Multidimensional Integrable Cosmological Models with Dynamical and Spontaneous Compactification

TL;DR

This paper explores multidimensional cosmological models with constant curvature spaces, providing exact solutions for dynamical and spontaneous compactification, especially in Ricci flat internal spaces, through classical and quantum analyses.

Contribution

It introduces integrable models with Ricci flat internal spaces and exact solutions for positive curvature external spaces, advancing understanding of compactification mechanisms.

Findings

Models are integrable when internal spaces are Ricci flat.

Exact solutions demonstrate dynamical and spontaneous compactification.

Quantum analysis complements classical results.

Abstract

Multidimensional cosmological models with $n (n > 1)$ spaces of constant curvature are discussed classically and with respect to canonical quantization. These models are integrable in the case of Ricci flat internal spaces. For positive curvature in the external space we find exact solutions modelling dynamical as well as spontaneous compactification of internal spaces.