7D Randall-Sundrum cosmology, brane-bulk energy exchange and holography

Abstract

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.Comment: 82 pages, 6 figures. Version accepted for publication; clarifications added in eq.(4), section VII.D, below eq.(102) and in appendix A; references adde