A gravity-driven inflation is shown to arise from a simple higher dimensional universe .
In vacuum , the shear of n > 1 contracting dimensions is able to inflate the remaining three spatial dimensions .
Said another way , the expansion of the 3-volume is accelerated by the contraction of the n -volume .
Upon dimensional reduction , the theory is equivalent to a four dimensional cosmology with a dynamical Planck mass .
A connection can therefore be made to recent examples of inflation powered by a dilaton kinetic energy .
Unfortunately , the graceful exit problem encountered in dilaton cosmologies will haunt this cosmology as well .

98.80.Hw , 98.80.Cq,04.50.+h

to be published in Phys .
Lett B