  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 of space expansion. 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.
