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One important prediction of a cosmological model based on grand unified theories is the production of primordial black holes and wormholes through a first order phase transition. In this paper we estimate the abundance of these holes and their effects on cosmology. We show that they play several important roles in the subsequent evolution of the universe and that the observational information of the present universe, conversely, yields constraints on the phenomenological parameters in grand unified theories. Especially we find that both the thermal and quantum nucleations of vacuum bubbles are the necessary ingredients in construct ing a cosmological model consistent with the present observations. 1.
Kodama et al. (Wed,) studied this question.