  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.
