SEMICLASSICAL APPROACH TO STABILITY OF EXTRA-DIMENSIONAL SPACES

We investigate the stability of extra-dimensional spaces after the inf lationary period within the framework of canonical quantum gravity. Si nce the four-dimensional spacetime has expanded to a sufficiently larg e size, a semiclassical treatment is appropriate. We propose a formula tion which takes into account the peculiarity of the inflation fields that their potential them depends on the gravitational constant. It is applied to the Kaluza-Klein theory with the Einstein-Hilbert action. The result indicates that the internal spaces are not stable.