Remarks on dynamical stabilization of internal spaces in multidimensional cosmology

The possibility of dynamical stabilization of an internal space is investigated for a multidimensional cosmological model with minimal coupled scalar field as the inflaton. It is shown that a successful dynamical compactification crucially depends on the type of interaction between the geometrical modulus field and the inflaton and its decay products. In the considered model a stable compactification can be ensured via trapping of the modulus field by a minimum of the effective potential.