  We investigate the cosmological expansion of the 3D space in a 6D model
compactified on a sphere, beyond the 4D effective theory analysis. We focus on
a case that the initial temperature is higher than the compactification scale.
In such a case, the pressure for the compact space affects the moduli dynamics
and induces the moduli oscillation even if they are stabilized at the initial
time. Under some plausible assumptions, we derive the explicit expressions for
the 3D scale factor and the moduli background in terms of analytic functions.
Using them, we evaluate the transition times between different cosmological
eras as functions of the model parameters and the initial temperature.
