  Recently there has been considerable interest in field theories and string
theories with large extra spacetime dimensions. In this paper, we explore the
role of such extra dimensions for cosmology, focusing on cosmological phase
transitions in field theory and the Hagedorn transition and radius
stabilization in string theory. In each case, we find that significant
distinctions emerge from the usual case in which such large extra dimensions
are absent. For example, for temperatures larger than the scale of the
compactification radii, we show that the critical temperature above which
symmetry restoration occurs is reduced relative to the usual four-dimensional
case, and consequently cosmological phase transitions in extra dimensions are
delayed. Furthermore, we argue that if phase transitions do occur at
temperatures larger than the compactification scale, then they cannot be of
first-order type. Extending our analysis to string theories with large internal
dimensions, we focus on the Hagedorn transition and the new features that arise
due to the presence of large internal dimensions. We also consider the role of
thermal effects in establishing a potential for the radius of the compactified
dimension, and we use this to propose a thermal mechanism for generating and
stabilizing a large radius of compactification.

High Energy Physics - Phenomenology;Astrophysics;High Energy Physics - Theory