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

TL;DR

This paper explores the cosmological dynamics of a 7D Randall-Sundrum model with brane-bulk energy exchange, constructs its holographic dual as a 6D CFT coupled to gravity, and analyzes the implications of non-conformal interactions.

Contribution

It extends the holographic duality framework to non-conformal, interacting scenarios with energy exchange, providing analytical and numerical insights into 7D RS cosmology.

Findings

Derived the holographic dual as an anomalous 6D CFT coupled to gravity.

Analyzed the critical points of the brane cosmology.

Connected bulk energy exchange to interactions in the dual theory.

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.