  We conjecture that the extra dimensions are physical non-compact at high
energy scale or high temperature; after the symmetry breaking or cosmological
phase transition, the bulk cosmological constant may become negative, and then,
the extra dimensions may become physical compact at low energy scale. We show
this in a five-dimensional toy brane model with three parallel 3-branes and a
real bulk scalar whose potential is temperature dependent. We also point out
that after the global or gauge symmetry breaking, or the supersymmetry breaking
in supergravity theory, the spontaneous physical compactification of the extra
dimensions might be realized.
