Holography for inflation using conformal perturbation theory

Abstract

We provide a precise and quantitative holographic description of a class of inflationary slow-roll models. The dual QFT is a deformation of a three-dimensional CFT by a nearly marginal operator, which, in the models we consider, generates an RG flow to a nearby IR fixed point. These models describe hilltop inflation, where the inflaton rolls from a local maximum of the potential in the infinite past (corresponding to the IR fixed point of the dual QFT) to reach a nearby local minimum in the infinite future (corresponding to the UV of the dual QFT). Through purely holographic means, we compute the spectra and bispectra of scalar and tensor cosmological perturbations. The QFT correlators to which these observables map holographically may be calculated using conformal perturbation theory, even when the dual QFT is strongly coupled. Both the spectra and the bispectra may be expressed this way in terms of CFT correlators that are fixed, up to a few constants, by conformal invariance. The form of slow-roll inflationary correlators is thus determined by the perturbative breaking of the de Sitter isometries away from the fixed point. Setting the constants to their values obtained by AdS/CFT at the fixed point, we find exact agreement with known expressions for the slow-roll power spectra and non-Gaussianities.