Superstring gravity and the early universe

Ten-dimensional superstring theories have been proposed as candidates for a unified description of all the forces of nature. These theories reduce to Einstein gravity coupled to Yang-Mills interactions at energy scales small compared to the string tension. The phenomenologically promising superstring theory, the heterotic string, is investigated at the high temperatures and short distances relevant in the early universe. The massive string modes alone constitute an unstable thermodynamic system with negative specific heat. The conditions for equilibrium between the massive string modes and the massless modes (radiation) are derived. The large energy fluctuations of the system require the use of the microcanonical ensemble. There is a maximum temperature which exceeds the temperature at which the canonical partition function becomes divergent. Above a critical volume there is a phase transition during which the massive string modes must evaporate. The possibilities of spontaneous compactification, large entropy production, and a solution of the horizon and flatness problems are discussed.