Abstract
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.
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