AdS/CFT and gravity

TL;DR

This paper explores how FRW cosmology can be derived from AdS/CFT correspondence, discusses gravity emergence, and sets bounds on AdS radius based on string theory and energy leakage estimates.

Contribution

It generalizes the AdS/CFT prescription for Green's functions and relates gravity strength to higher-dimensional parameters, providing new insights into holographic cosmology.

Findings

FRW cosmology emerges as a hypersurface in AdS-Schwarzschild space.

Gravity strength G_4 is related to G_5 and AdS radius L.

Bounds on AdS radius L are set based on string theory and energy leakage estimates.

Abstract

The radiation-dominated k=0 FRW cosmology emerges as the induced metric on a codimension one hypersurface of constant extrinsic curvature in the five-dimensional AdS-Schwarzschild solution. That we should get FRW cosmology in this way is an expected result from AdS/CFT in light of recent comments regarding the coupling of gravity to "boundary" conformal field theories. I remark on how this calculation bears on the understanding of Randall and Sundrum's "alternative to compactification." A generalization of the AdS/CFT prescription for computing Green's functions is suggested, and it is shown how gravity emerges from it with a strength G_4 = 2 G_5/L. Some numerical bounds are set on the radius of curvature L of AdS_5. One of them comes from estimating the rate of leakage of visible sector energy into the CFT. That rate is connected via a unitarity relation to deviations from Newton's force law at short distances. The best bound on L obtained in this paper comes from a match to the parameters of string theory. It is L < 1 nm if the string scale is 1 GeV. Higher string scales imply a tighter bound on L.