We develop an inflationary model without small parameters on the basis of
multidimensional f(R) gravity with a minimally coupled scalar field. The
model is described by two stages. The first one begins at energy scales about
the D-dimensional Planck mass and ends with the de Sitter metric of our space
and the maximally symmetric extra dimensions. In the following, the quantum
fluctuations produce a wide set of inhomogeneous extra metrics in causally
disconnected regions quickly generated in the de Sitter space. We find a
specific extra space metric that leads to the effective Starobinsky model that
fits the observational data