Large radius generation and phase transitions in cosmology with extra dimensions

We consider the role of extra dimensions in cosmology, focusing on cosmological phase transitions in field theory and the Hagedorn transition and generation of a large compactification radius in string theory. We find that for temperatures larger than the compactification radii, cosmological phase transitions in field theory are delayed compared with the usual four-dimensional case. Furthermore, we argue that phase transitions in extra dimensions cannot be of the first-order type. In string theories with large internal dimensions, the Hagedorn temperature is a limiting temperature and gives rise to significant entropy production as the universe approaches this temperature. We also point out that string thermal effects give rise to an effective potential for the radius of the compactified dimension. This leads to a thermal mechanism for generating a large radius of compactification.