Spacetime evolution during moduli stabilization in radiation dominated era beyond 4D effective theory

TL;DR

This paper studies the spacetime evolution during moduli stabilization in a higher-dimensional model, revealing prolonged radiation effects and slower expansion than standard cosmology, especially when stabilization scales exceed compactification scales.

Contribution

It numerically analyzes the full higher-dimensional dynamics of moduli stabilization beyond the 4D effective theory, highlighting extended radiation influence and altered expansion rates.

Findings

Radiation remains significant longer than the stabilization time.

Expansion of non-compact space is slower than in matter-dominated universe.

Radiation's equation of state stays below 1/3, indicating extra-dimensional effects persist.

Abstract

We investigate the time evolution of the background spacetime during the moduli stabilization process, which is assumed to occur in the radiation dominated era. The setup is basically the Salam-Sezgin model, but we add a potential term for the dilaton in order to stabilize the moduli completely. We numerically solve the higher-dimensional background field equations, including a case that the stabilization process cannot be described within the 4D effective theory. In contrast to the conventional 4D effective theory analysis, we find that when the mass scale of the stabilization is larger than the compactification scale, the radiation contribution to the total energy density remains to be non-negligible for a much longer time than the stabilization time scale. As a result, the non-compact 3D space expands slower than the matter dominated universe. We also find the equation of state for the radiation $w_{\rm rad}$ remains to be smaller than 1/3 for a long time, which indicates that the radiation still feels the extra dimensions for a while even after the moduli are stabilized.