Dimensional reduction transition

In this conference on phase transitions in the early Universe the author discusses the transition from more than four space-time dimensions to four effective space-time dimensions; the dimensional reduction transition. The basic assumption is that the true dimensionality of space-time is more than four, and that at present the extra dimensions are compact and too small to be observable. The origin of the observed gauge symmetries from symmetries of a compact space has been proposed as a possible approach for the unification of particle physics and gravity. The common assumption in all models with extra dimensions is that the unseen dimensions are compactified to a very small size, usually taken to be of the order of the Planck length. To probe the structure of the extra dimensions would require energies of the Planck mass E = m/sub pl/ = 1.2 x 1019GeV, and the early Universe may be the only source of such energies. The author will assume for initial conditions that all spatial dimensions are small, and that initially the Universe had N = 3 + D spatial dimensions. When the temperature fell below T = R/sub D/-1, where R/sub D/ is the physical size of the compact extra dimensions, the space-time dimensionality of the Universe underwent a reduction to effectively a 4 space-time dimensional Universe, and dynamical effects of the extra dimensions became unimportant. In this paper I will discuss three possible consequences of this cosmological dimensional reduction; entropy production (inflation), magnetic monopole production, and stable, massive particle production. 14 refs., 4 figs