  We discuss the cosmological implications and the holographic dual theory of
the 7D Randall-Sundrum (RS) gravitational set-up. Adding generic matter in the
bulk on the 7D gravity side we study the cosmological evolution inferred by the
non vanishing value of the brane-bulk energy exchange parameter. This analysis
is achieved in detail for specific assumptions on the internal space evolution,
including analytical considerations and numerical results. The dual theory is
then constructed, making use of the holographic renormalization procedure. The
resulting renormalized 6D CFT is anomalous and coupled to 6D gravity plus
higher order corrections. The critical point analysis on the brane is
performed. Finally, we sketch a comparison between the two dual descriptions.
We moreover generalize the AdS/CFT dual theory to the non conformal and
interacting case, relating the energy exchange parameter of the bulk gravity
description to the new interactions between hidden and visible sectors.
