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

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-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.

Automated summary

This study investigates the time evolution of the background spacetime during the moduli stabilization process in the radiation dominated era. The findings suggest that when the mass scale of stabilization is larger than the compactification scale, the contribution of radiation to the total energy density remains significant for a longer time, resulting in slower expansion of the non-compact 3D space and continued perception of extra dimensions by radiation.