Cosmological phase transitions and radius stabilization in higher dimensions

Recently there has been considerable interest in field theories and string theories with large extra space-time dimensions. In this paper, we explore the role of such extra dimensions for cosmology, focusing on cosmological p hase transitions in field theory and the Hagedorn transition and radius sta bilization in string theory. In each case, we find that significant distinc tions emerge from the usual case in which such large extra dimensions are a bsent. For example, for temperatures larger than the scale of the compactif ication radii, we show that the critical temperature above which symmetry r estoration occurs is reduced relative to the usual four-dimensional case, a nd consequently cosmological phase transitions in extra dimensions are dela yed. Furthermore, we argue that if phase transitions do occur at temperatur es larger than the compactification scale, then they cannot be of first-ord er type. Extending our analysis to string theories with large internal dime nsions, we focus on the Hagedorn transition and the new features that arise due to the presence of large internal dimensions. We also consider the rol e of thermal effects in establishing a potential for the radius of the comp actified dimension, and we use this to propose a thermal mechanism for gene rating and stabilizing a large radius of compactification. (C) 1999 Elsevie r Science B.V.