Nonsingular multidimensional cosmologies with Lobachevsky spatial sections

TL;DR

This paper presents exact solutions for multidimensional cosmological models with hyperbolic geometry that are nonsingular and involve phantom scalar fields, leading to smooth evolution and bounces without fine tuning, inspired by string theory and Weyl gravity.

Contribution

It introduces new multidimensional cosmological models with hyperbolic geometry using phantom scalar fields, avoiding fine tuning and providing explicit solutions.

Findings

Models exhibit nonsingular bounces without fine tuning.

Extra dimensions and scalar fields evolve smoothly between finite values.

Examples derived from string-inspired and Weyl gravity theories.

Abstract

Examples of nonsingular cosmological models are presented on the basis of exact solutions to multidimensional gravity equations. These examples involve pure imaginary scalar fields, or, in other terms, ``phantom'' fields with an unusual sign of the kinetic term in the Lagrangian. We show that, with such fields, hyperbolic nonsingular models with a cosmological bounce (unlike spherical and spatially flat models) emerge without special relations among the integration constants, i.e., without fine tuning. In such models, the extra-dimension scale factors as well as scalar fields evolve smoothly between different finite asymptotic values. Examples of theories which create phantom scalar fields are obtained from string-inspired multidimensional field models and from theories of gravity in integrable Weyl space-times.