  Starting from pure multidimensional gravity with curvature-nonlinear terms
but no matter fields in the initial action, we obtain a cosmological model with
two effective scalar fields related to the size of two extra factor spaces. The
model includes both an early inflationary stage and that of modern accelerated
expansion and satisfies the observational data. There are no small parameters;
the effective inflaton mass depends on the initial conditions which explain its
small value as compared to the Planck mass. At the modern stage, the size of
extra dimensions slowly increases, therefore this model predicts drastic
changes in the physical laws of our Universe in the remote future.
