Full higher-dimensional analysis of moduli oscillation and radiation in expanding universe

Abstract

Abstract We investigate effects of the radiation and the moduli oscillation around the stabilized values on the evolution of a 6-dimensional spacetime compactified on S2. In order to see the transition from the 5-dimensional space to the 3-dimensional one, we develop a procedure to pursue the spacetime evolution with appropriate approximations, which is valid until the spacetime behaves like 4-dimensional. In the case that the moduli stabilization process cannot be described in the context of the 4-dimensional effective theory, it takes quite a long time for the moduli oscillation to dominate the total energy density, in contrast to the conventional result obtained by the 4-dimensional effective theory approach. We also found that even if the moduli are set at the stabilized values, they start to oscillate due to the pressure in the extra space S2 in some cases.