AdS/CFT and gravity

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 the Randall-Sundrum ``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 ${G}_{4}{=2G}_{5}/L.$ Some upper bounds are set on the radius of curvature L of ${\mathrm{AdS}}_{5}.$ 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 $L\ensuremath{\lesssim}1\mathrm{nm}$ if the string scale is $1\mathrm{GeV}.$ Higher string scales imply a tighter bound on L.