Abstract:
It is shown that, with the only exception of n = 2, the Einstein-Hilbert action in n + D + d dimensions, with n times, is invariant under the duality transformation a --> 1/a and b --> 1/b, where a is a Friedmann-Robertson-Walker scale factor in D dimensions and b a Brans-Dicke scalar field in d dimensions respectively. We investigate the (2 + D + d)-dimensional cosmological model in some detail.