We consider a toy cosmological model in string theory involving the winding and momentum modes of (m,n) strings, i.e. bound states of m fundamental and n D-strings. The model is invariant under S-duality provided that m and n are interchanged. The dilaton is naturally stabilized due to S-duality invariance, which offers a new mechanism of moduli fixing in string gas cosmology. Using a tachyon field rolling down to its ground state, we also point out a possible way of realizing a cosmological phase with decreasing Hubble radius and constant dilaton.

6 pages, revtex4, v2: references and comments added