Integrable Cosmological Models From Higher Dimensional Einstein Equations

TL;DR

This paper explores higher-dimensional cosmological models derived from Einstein equations, revealing integrability conditions linked to superstring and M-theory, and analyzes acceleration in universes with negatively curved spaces.

Contribution

It identifies the specific total dimensions (D=10 or D=11) for integrability and provides analytic solutions in the four-dimensional Einstein frame.

Findings

Integrability occurs only in D=10 or D=11 dimensions.

Analytic solutions are obtained for generic initial conditions.

Accelerating universe solutions are studied with negative curvatures.

Abstract

We consider the cosmological models for the higher dimensional spacetime which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological equations is that the total space-time dimensions are D=10 or D=11 which is exactly the conditions for superstrings or M-theory. We obtain analytic solutions with generic initial conditions in the four dimensional Einstein frame and study the accelerating universe when both our space and the internal space have negative curvatures.