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Abstract
The three phase transitions (the GUT, the electroweak and the quark-hadron), which the universe is assumed to have undergone, produce very important physical effects if they are assumed to be of first-order. It is also important that enough supercooling is produced at these transitions so that the rate of nucleation of the lower temperature phase out of the higher temperature phase is large. We argue on the basis of finitesize scaling theory that for the quark-hadron and the electroweak phase transitions the universe does not supercool enough to give sizeable nucleation rates. The nucleation probability seems to be significant only for the GUT transition.
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