SUPERCOOLING AND NUCLEATION IN PHASE-TRANSITIONS OF THE EARLY UNIVERSE

The three phase transitions (the GUT, the electroweak and the quark-ha dron), which the universe is assumed to have undergone, produce very i mportant physical effects if they are assumed to be of first-order. It is also important that enough supercooling is produced at these trans itions so that the rate of nucleation of the lower temperature phase o ut of the higher temperature phase is large. We argue on the basis of finite-size scaling theory that for the quark-hadron and the electrowe ak phase transitions the universe does not supercool enough to give si zeable nucleation rates. The nucleation probability seems to be signif icant only for the GUT transition.