A Scenario for the Dimensional Compactification in Eleven-Dimensional Space-Time

TL;DR

This paper proposes a scenario where, near the cosmological singularity, an 11-dimensional universe naturally evolves into a 3-dimensional expanding space and a 7-dimensional compactified space, supporting theories of unification.

Contribution

It introduces a multidimensional mixmaster model that describes dimensional compactification in 11-dimensional space-time near singularities, with a conformal factor to ensure a finite universe expansion.

Findings

Universe expands with power-law inflation

4-curvature divergences are removed by a conformal factor

Supports geometrical unification theories in 11D space-time

Abstract

We discuss the inhomogeneous multidimensional mixmaster model in view of appearing, near the cosmological singularity, a scenario for the dimensional compactification in correspondence to an 11-dimensional space-time. Our analysis candidates such a collapsing picture toward the singularity to describe the actual expanding 3-dimensional Universe and an associated collapsed 7-dimensional space. To this end, a conformal factor is determined in front of the 4-dimensional metric to remove the 4-curvature divergences and the resulting Universe expands with a power-law.inflation. Thus we provide an additional peculiarity of the eleven space-time dimensions in view of implementing a geometrical theory of unification.