EVOLUTION OF THE DENSITY PARAMETER IN MULTIDIMENSIONAL COSMOLOGY

Inflation as a dynamical effect of extra dimensions is discussed from the viewpoint of the evolution of the parameters OMEGA and q in the physical space. By reducing the dynamics of the models FLRW (k = +/-1) X T(D)(T(D) = S1 X . . . X S1) and FLRW (k = 0) X S(D), where FLRW denotes Friedmann, Lemaitre, Robertson, and Walker, to two dimensions it is shown that inflation need not imply OMEGA congruent-to 1 for the present time, i.e., that it does not solve the flatness problem. The energy-momentum tensor of the form T(nu)mu = (rho,mrho,mrho,mrho,nrho, . . . , nrho) is assumed. The results are comparable to those obtained by Madsen and Ellis for four-dimensional models N = 1, d = 11 of supergravity theory.