On the dual flow of slow-roll inflation

Abstract

We study the dual 3d Euclidean RG flow of single-field slow-roll Inflation using the postulates of the dS/CFT correspondence. For that purpose we solve for the inflationary fluctuation at all times using a matching procedure between two approximate solutions which are separately valid at different regions of the space of parameters but together cover all of it. The two modes of the full solution mix such that each of the modes at late times is a superposition of the modes in the quasi-de Sitter region. We find that the dual theory admits two phases of explicit and spontaneous breaking of conformal symmetry.We also find that the mixing effect between the two modes in the bulk implies that slowroll inflation does not guarantee, but rather generically generates, a nearly scale invariant power spectrum, except in fine-tuned situations. We suggest that the mixing effect can have a unique signature on other cosmological observables such as the bispectrum.

An effective theory for holographic RG flows

“…Thus our approach may be viewed as intermediate between a general conformal symmetry analysis [5][6][7][8][9] and the study of particular holographic examples (see [10] for a review and many older references e.g. [11], and also the recent work [12][13][14][15]) for the study of the low-energy τ action. We will be able to determine universal properties of this action by constructing a bulk π action and solving the equations of motion for π.…”

“…This is the AdS analogue [15] of slow roll inflation [20,21]. We will make frequent use of this setup in our future discussions, especially when we study QFTs in dimension d > 2, since it will simplify the computations considerably.…”

“…In the usual top-down approach to the study of holographic RG flows [10,12,13,15,[25][26][27][28], one needs to specify the bulk action and then solve the background equations of motions for the matter fields and the geometry. The obvious drawbacks of such an approach are that we lack a general rule for what types of potentials and interactions to use in order to generate an RG flow for the boundary theory, and that for given holographic RG models, the process of finding background profiles can be computationally cumbersome.…”

“…An intuitive example in the opposite limit would be an extremely thick 'domain wall', where φbg φ bg Ȧ. This is the AdS analogue [12] of slow roll inflation [17,18]. We will make frequent use of this setup in our future discussions, especially when we study QFTs in dimension d > 2, since it will simplify the computations considerably.…”

“…In this note we will study holographic renormalization flows by erecting a general holographic effective field theory for π, the goldstone boson of the broken spacetime symmetry dual to dilatations. Thus our approach may be viewed as intermediate between a general conformal symmetry analysis [5][6][7][8] and the study of particular holographic examples (see [9] for a review and many older references, and also the recent work [10][11][12]) for the study of the low-energy τ action. We will be able to determine universal properties of this action by constructing a bulk π action and solving the equations of motion for π.…”