In a previous question I mentioned how a calculation performed by Chodos an Detweiler in the late 1970's began with a model universe in 5 dimensional space-time, and the general relativistic solution showed that the model was unstable to expanding in 4 of these dimensions and collapsing in the fifth.
The 5th dimension is space-like, but eventually ends up having a size of about the Planck scale of 10^-33 centimeters or so. I seem to recall further studies of this 'dimensional compactification' process in even higher dimensions being used to drive the inflation process. The idea is that you start out with a space-time in some large number of dimensions, and an event ( probably quantum tunneling) spontaneously initiates the compactification process, and that the collapse of the dimensions greater than 3+1=4 triggers the inflating of the remaining 4 dimensions to make them the 'large' ones we now see. Presumably the additional dimensions are still with us as the extended set of dimensions to space-time that are needed by the superstring theorists to unify all the other phenomena in physics.
But this, of course, is all just speculation. We do not really have any proof that space-time operates this way, or is anything other than the 4-dimensional 'thing' our senses tell us it is.
Copyright 1997 Dr. Sten Odenwald
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