DYNAMICAL SOLUTIONS TO THE HORIZON AND FLATNESS PROBLEMS

We discuss in some detail the requirements on an early-Universe model that solves the horizon and flatness problems during the epoch of clas sical cosmology (t greater-than-or-equal-to t(i) >> 10(-43) sec). We s how that a dynamical resolution of the horizon problem requires superl uminal expansion (or very close to it) and that a truly satisfactory r esolution of the flatness problem requires entropy production. This im plies that a proposed class of adiabatic models in which the Planck ma ss varies by many orders of magnitude cannot fully resolve the flatnes s problem. Furthermore, we show that, subject to minimal assumptions, such models cannot solve the horizon problem either. Because superlumi nal expansion and entropy production are the two generic features of i nflationary models, our results suggest that inflation, or something v ery similar, may be the only dynamical solution to the horizon and fla tness problems.