Classical evolution of subspaces

TL;DR

This paper investigates how the evolution of high-energy manifolds depends on their dimensions and initial conditions, revealing that simple symmetric models are insufficient and that complex solutions like funnels can arise.

Contribution

It provides an analytical and numerical analysis of manifold evolution with higher-derivative gravity, highlighting the importance of initial conditions and dimensionality in final universe configurations.

Findings

Maximally symmetric manifolds' growth depends on dimensionality

Simple symmetric extra spaces are insufficient to describe our universe

Initial conditions can lead to complex solutions like funnels

Abstract

We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. A number of final metrics describing our Universe is quite poor if we limit ourselves with a maximally symmetric extra space. We show that the initial conditions can be a reason of nontrivial solutions (funnels) and study their properties.