  We discuss in some detail the requirements on an early-Universe model that
solves the horizon and flatness problems during the epoch of classical
cosmology ($t\ge t_i\gg 10^{-43}\sec$). We show that a dynamical resolution of
the horizon problem requires superluminal expansion (or very close to it) and
that a truly satisfactory resolution of the flatness problem requires entropy
production. This implies that a proposed class of adiabatic models in which the
Planck mass varies by many orders of magnitude cannot fully resolve the
flatness problem. Furthermore, we show that, subject to minimal assumptions,
such models cannot solve the horizon problem either. Because superluminal
expansion and entropy production are the two generic features of inflationary
models, our results suggest that inflation, or something very similar, may be
the only dynamical solution to the horizon and flatness problems.
