Full higher-dimensional analysis of moduli oscillation and radiation in expanding universe

TL;DR

This paper explores the complex evolution of a 6-dimensional universe with stabilized extra dimensions, focusing on how radiation and moduli oscillations influence the transition to a 4-dimensional spacetime, revealing limitations of 4D effective theories.

Contribution

It develops a method to analyze the spacetime evolution from 6D to 4D, highlighting scenarios where 4D effective theories fail to describe moduli stabilization and oscillation dynamics.

Findings

Moduli oscillation can dominate energy density longer than predicted by 4D theories.

Moduli can start oscillating due to pressure in extra dimensions even when initially stabilized.

Transition to 4D spacetime involves complex dynamics not captured by simplified models.

Abstract

We investigate effects of the radiation and the moduli oscillation around the stabilized values on the evolution of a 6-dimensional spacetime compactified on $S^2$. In order to see the transition from the 5-dimensional space to the 3-dimensional one, we develop a procedure to pursue the spacetime evolution with appropriate approximations, which is valid until the spacetime behaves like 4-dimensional. In the case that the moduli stabilization process cannot be described in the context of the 4-dimensional effective theory, it takes quite a long time for the moduli oscillation to dominate the total energy density, in contrast to the conventional result obtained by the 4-dimensional effective theory approach. We also found that even if the moduli are set at the stabilized values, they start to oscillate due to the pressure in the extra space $S^2$ in some cases.