Stability of extra dimensions in O(d,d)-covariant string gas cosmology

Abstract

String theory is one of the most promising candidates for theory of quantum gravity. String gas cosmology is thus expected to be a plausible cosmological model which provides an excellent explanation for dynamics of the early universe. By means of T-duality and string winding modes, string gas cosmology can solve the initial singularity problem and the dimensionality problem in standard cosmology. According to Brandenberger-Vafa mechanism, the annihilation process of winding and anti-winding modes can take place effectively in four-dimensional spacetime. As a consequence, the expansion of three spatial dimensions comes with the evolution of the early universe; on the other hand, six extra dimensions are stabilized at the self-dual point due to the existence of momentum and winding modes in these directions. Despite its success, string gas cosmology encounters the moduli stabilization problem concerning the stability of moduli describing size, shape and, flux of extra dimensions for the late-time universe. The numerical calculation from the previous work based on the assumption of the vanishing flux showed that the size of the extra dimensions dampedly oscillated around the self-dual point as the dilaton ran slowly to weak coupling. The aim of this thesis is to study string gas cosmology in the O(d,d)-covariant formalism and resolve the moduli stabilization problem qualitatively. In this thesis we considered the generators and the enhanced symmetric fixed points of O(d,d;ℤ) symmetry, which is regarded as a generalization of T-duality for d-dimensional toroidal background with the non-vanishing flux. The result showed that in the case of two-dimensional toroidal extra dimensions, there were two enhanced symmetric fixed points corresponding to the simply laced groups, SU(2)xSU(2), and SU(3), and the dilaton was stabilized by Hubble damping term at both fixed points.