Mathematics – Logic
Scientific paper
Nov 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984stin...8530990k&link_type=abstract
Presented at the Intern. Symp. on Phase Transitions in the Very Early Universe, Bielefeld, West Germany, 1 Jun. 1984
Mathematics
Logic
Cosmology, Gauge Invariance, Magnetic Monopoles, Particle Production, Relativity, Unified Field Theory, Entropy, Gravitation Theory, Plancks Constant, Space, Time
Scientific paper
The transition from more than four space-time dimenisons to four effective space-time dimensions, the dimensional reduction transition is discussed. 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 lenght. To probe the structure of the extra dimensions would require energies of the Planck mass E = mp1 = 1.2 x 1019GeV, and the early Universe may be the only source of such energies. It is assummed 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 = (RD-1), where RD is the physical size of the compact extra dimensions, the space-time dimensionality of the Universe, and dynamical effects of the extra dimensions became unimportant. Three possible consequences of this cosmological dimensional reduction are discussed; entropy production (inflation), magnetic monopole production, and stable, massive particle production.
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