Non-singular cosmological models in string gravity with constant dilaton and second-order curvature corrections

We investigate FRW cosmological solutions in the theory of a modulus field coupled to gravity through a Gauss-Bonnet term. The explicit analytical forms of non-singular asymptotics are presented for power-law and exponentially steep modulus coupling functions. We study the influence of a modulus field potential on these asymptotic regimes and find some forms of the potential which do not destroy the non-singular behaviour. In particular, we obtain that exponentially steep coupling functions arising from the string theory do not allow non-singular past asymptotic unless the modulus field potential tends to zero for a modulus field psi --> +/-infinity. Finally, the modification of the chaotic dynamics in the closed FRW universe due to presence of the Gauss-Bonnet term is discussed.