Consistency condition for inflation from (broken) conformal symmetry

Abstract

We investigate the symmetry constraints on the bispectrum, i.e. the three-point correlationfunction of primordial density fluctuations, in slow-roll inflation.It follows from the defining property of slow-roll inflation that primordial correlation functions inherit most of their structure from weakly broken de Sitter symmetries.Using holographic techniques borrowed from the AdS/CFT correspondence, the symmetry constraints on the bispectrum can be mapped to a set of stress-tensor Ward identities in a weakly broken 2+1-dimensional Euclidean CFT.We construct the consistency condition from these Ward identities using conformal perturbation theory.This requires a second order Ward identity and the use of the evolution equation. Our result also illustrates a subtle difference between conformal perturbation theory and the slow-roll expansion.