Abstract
The promise of the inflationary Universe scenario is to free the present state of the Universe from extreme dependence on initial data. Paradoxically, inflation is usually analyzed in the context of the homogeneous and isotropic Robertson-Walker (RW) cosmological models. We show that all but a small subset of the homogeneous models (the Bianchi models) undergo inflation. Any initial anisotropy is so strongly damped that if sufficient inflation occurs to solve the flatness/horizon problems the Universe today would still be very isotropic. Some of the Bianchi models will eventually (in the exponentially distant future) become very anisotropic again. 15 refs.
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