Brane New World

TL;DR

The paper analyzes a Randall-Sundrum cosmology with a domain wall in $AdS_5$ carrying a large-$N$ CFT, where the conformal anomaly induces an effective wall tension that yields a de Sitter wall. By leveraging the AdS/CFT correspondence and the no-boundary proposal, the authors compute the graviton two-point function on the wall, finding that CFT quantum loops strongly suppress tensor perturbations at small angular scales while preserving the de Sitter background. They show consistency with four-dimensional gravity in the limit $N\gg N_{RS}$, with corrections controlled by $N_{RS}^2/N^2$, and identify discrete tensor modes arising from the wall coupling. The results imply that in inflationary scenarios with many matter fields, small-scale tensor fluctuations could be much smaller than in standard calculations, potentially affecting CMB polarization and providing observational handles on high-energy physics and holographic cosmology.

Abstract

We study a Randall-Sundrum cosmological scenario consisting of a domain wall in anti-de Sitter space with a strongly coupled large $N$ conformal field theory living on the wall. The AdS/CFT correspondence allows a fully quantum mechanical treatment of this CFT, in contrast with the usual treatment of matter fields in inflationary cosmology. The conformal anomaly of the CFT provides an effective tension which leads to a de Sitter geometry for the domain wall. This is the analogue of Starobinsky's four dimensional model of anomaly driven inflation. Studying this model in a Euclidean setting gives a natural choice of boundary conditions at the horizon. We calculate the graviton correlator using the Hartle-Hawking ``No Boundary'' proposal and analytically continue to Lorentzian signature. We find that the CFT strongly suppresses metric perturbations on all but the largest angular scales. This is true independently of how the de Sitter geometry arises, i.e., it is also true for four dimensional Einstein gravity. Since generic matter would be expected to behave like a CFT on small scales, our results suggest that tensor perturbations on small scales are far smaller than predicted by all previous calculations, which have neglected the effects of matter on tensor perturbations.

Figures (2)

• Figure 1: Carter-Penrose diagram of anti-de Sitter space with a flat domain wall. The dotted line denotes timelike infinity and the arrows denote identifications. The heavy dots denote points at infinity. Note that the Cauchy horizons intersect at infinity.
• Figure 2: Anti-de Sitter space with a de Sitter domain wall. AdS is drawn as a solid cylinder, with the boundary of the cylinder (dashed line) representing timelike infinity. The light cone shown is the horizon. The arrows denote identifications.