Effective action for the homogeneous radion in brane cosmology

We consider cosmological two-brane models with AdS bulk, for which the radion, i.e., the separation between the two branes, is time dependent. In the case of two de Sitter branes (including Minkowski branes, as a limiting case), we compute explicitly, without any approximation, the effective four-dimensional action for the radion. With the scale factor on-shell, this provides the non-perturbative dynamics for the radion. We discuss the differences between the dynamics derived from the four-dimensional action with the scale factor off-shell and the true five-dimensional dynamics. (C) 2002 Published by Elsevier Science B.V.