Inflationary Perturbations from Deformed CFT

TL;DR

The paper investigates how the spectrum of inflationary perturbations can be derived from a deformed CFT via the dS/CFT correspondence, treating cosmological evolution as a holographic RG flow governed by the Callan-Symanzik equation. By relating bulk expectation values to boundary correlators and incorporating RG flow, it shows that the scalar power spectrum scales as $P_R ∝ H^2 k^{−2λ}$ with $λ = Δ-3$, and that the spectral tilt satisfies $n_s-1 ≈ -β^2 - 2λ$ to leading order, with $β$ and $λ$ tied to slow-roll observables. The work emphasizes the universality of the inflationary spectrum, arguing that holography in a timelike direction decouples the spectrum from subhorizon microphysics and makes RG flow the controlling mechanism for deviations from scale invariance. It also provides a concrete framework to compute corrections beyond the fixed point via RG-flow equations, linking boundary CFT data to cosmological observables and clarifying the role of holography in de Sitter space.

Abstract

We present a new method to calculate the spectrum of (slow-roll) inflationary perturbations, inspired by the conjectured dS/CFT correspondence. We show how the standard result for the spectrum of inflationary perturbations can be obtained from deformed CFT correlators, whose behavior is determined by the Callan-Symanzik equation. We discuss the possible advantages of this approach and end with some comments on the role of holography in dS/CFT and its relation to the universal nature of the spectrum of inflationary perturbations.