What is the Dimension of the Universe?

Abstract

We discuss the concept of dimension in its mathematical and cosmological bearings. According to Kaluza-Klein and superstring theories the Universe is fu lly N-dimensional /with N> 3/ but all except three spatial dimensions are confined to sizes close to the Planck length. As the energies necessary to probe the extra spatial dimensions are not attainable in terrestrial accelerators, it is natural to use the Big Bang to study the effect of extra dimensions. The particular cosmology we present here is the /Priedman-Robertson-Walker/ x /n-sphere/ universe. The cosmological evolution of such a world with n + 3 spatial dimensions can be studied using higher-dimensional extensions of general relativity . It turns out that, within the class of both vacuum and radiation filled models, the qualitative features of the universe do not depend on the specific number of dimensions and, particulary, the cosmological dimensional- reduction occurs, i.e., the universe passess from multi- dimensional phase to the Friedman-like one. However, at present there is no theoretical explanation why just three dimensions have expanded to a large size.