Anisotropic cosmological dynamics in Einstein-Gauss-Bonnet gravity: an example of dynamical compactification in 7+1 dimensions

TL;DR

This paper demonstrates how a 7+1 dimensional anisotropic universe naturally evolves into a product of expanding and stabilized subspaces within Einstein-Gauss-Bonnet gravity, without fine-tuning initial conditions.

Contribution

It provides an analytical and numerical analysis of dynamical compactification in higher-dimensional gravity, showing the emergence of stabilized internal dimensions.

Findings

Universe evolves towards a product of isotropic subspaces

Dynamical compactification occurs without fine-tuning for certain parameters

Analytical conditions for stabilization are confirmed numerically

Abstract

We consider a particular example of dynamical compactification of an anisotropic 7+1 dimensional Universe in Einstein - Gauss - Bonnet gravity. Starting from rather general totally anisotropic initial conditions a Universe in question evolves towards a product of two isotropic subspaces. The first subspace expands isotropically, the second represents an "inner" isotropic subspace with stabilized size. The dynamical evolution does not require fine-tuning of initial conditions, though it is possible for a particular range of coupling constants. The corresponding condition have been found analytically and have been confirmed using numerical integration of equations of motion.