Gravitational excitons from extra dimensions

Inhomogeneous multidimensional cosmological models with a higher-dimensional space-time manifold M=M₀×∏ᵢ₌₁ⁿMᵢ $(n>~1)$ are investigated under dimensional reduction to D₀-dimensional effective models. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces near minima of an effective potential can be observed as massive scalar fields in the external space-time. Parameters of models that ensure minima of the effective potentials are obtained for particular cases and masses of gravitational excitons are estimated.