Moduli Stabilization in String Gas Compactification

We investigate the moduli stabilization in string gas compactification. We first present a numerical evidence showing the stability of the radion and the dilaton. To understand this numerical result, we construct the 4-dimensional effective action by taking into account T-duality. It turns out that the dilaton is actually marginally stable. When the moduli other than the dilaton is stabilized at the self-dual point, the potential for the dilaton disappears and then the dilaton is stabilized due to the hubble damping. In order to investigate if this mechanism works in more general cases, we analyze the stability of $T_2 \otimes T_2 \otimes T_2$ compactification in the context of massless string gas cosmology. We found that the volume moduli, the shape moduli, and the flux moduli are stabilized at the self dual point in the moduli space. Thus, it is proved that this simple compactification model is stable.