  A Gauss-Bonnet term naturally appears in the action for gravity when one
considers the existence of space time with dimensions more than 1+3. A variety
of inflationary models can be obtained within such a framework, once the scale
factor for the hidden dimension(s) is not constrained to be the same as that of
the visible ones. In particular, the need for an adhoc inflaton field is
eliminated. The phase space has a rich structure with different types of
solutions, both stable and unstable. For a large class of solutions, the scale
factors rapidly approach an asymptotic exponential form. Furthermore,
sufficient inflation can be obtained for only a modest compression of the
hidden world, if the latter is of a sufficiently large dimension.
