Randall-Sundrum II Cosmology, AdS/CFT, and the Bulk Black Hole

TL;DR

This paper investigates Randall-Sundrum II cosmology with a brane-localized Standard Model and a 5D AdS bulk, analyzing bulk graviton radiation and the formation of bulk AdS-Schwarzschild black holes, and connects the evolution to an AdS/CFT description. By computing graviton-production cross sections and integrating over the thermal spectrum, the authors quantify dark radiation as $\Omega_{d,N}\simeq 0.005$ during the $\rho$-dominated era and up to $\Omega_{d,N}\lesssim 0.05$ for an extended $\rho^2$ epoch. They show that the AdS/CFT formulation reproduces the $\rho^2$ correction at low densities via higher-derivative terms ${\cal R}_2$ with coefficient $b_4$, but emphasize that the UV completion (e.g., AdS$_5$ vs AdS$_5\times S^5$) controls whether the $\rho^2$ regime is physically accessible. Overall, the work clarifies how dark radiation and higher-curvature effects arise in RSII and discusses potential observational signatures and the importance of the UV definition.

Abstract

We analyse the cosmology of a brane world model where a single brane carrying the standard model fields forms the boundary of a 5-dimensional AdS bulk (the Randall-Sundrum II scenario). We focus on the thermal radiation of bulk gravitons, the formation of the bulk black hole, and the holographic AdS/CFT definition of the RSII theory. Our detailed calculation of bulk radiation reduces previous estimates to a phenomenologically acceptable, although potentially visible level. In late cosmology, in which the Friedmann equation depends linearly on the energy density ρ, only about 0.5% of energy density is lost to the black hole or, equivalently, to the `dark radiation' (Ω_{d,N} \simeq 0.005 at nucleosynthesis). The preceding, unconventional ρ^2 period can produce up to 5% dark radiation (Ω_{d,N} <\sim 0.05). The AdS/CFT correspondence provides an equivalent description of late RSII cosmology. We show how the AdS/CFT formulation can reproduce the ρ^2 correction to the standard treatment at low matter density. However, the 4-dimensional effective theory of CFT + gravity breaks down due to higher curvature terms for energy densities where ρ^2 behaviour in the Friedmann equation is usually predicted. We emphasize that, in going beyond this energy density, the microscopic formulation of the theory becomes essential. For example, the pure AdS_5 and string-motivated AdS_5\timesS^5 definitions differ in their cosmological implications.