Consistency condition for inflation from (broken) conformal symmetry

TL;DR

This paper derives symmetry-based constraints on the primordial bispectrum in slow-roll inflation using holographic methods and conformal perturbation theory, revealing subtle differences from the slow roll expansion.

Contribution

It introduces a novel approach to derive inflationary consistency conditions via holography and stress-tensor Ward identities, connecting inflationary correlators to conformal field theory techniques.

Findings

Derived the inflationary bispectrum consistency condition from Ward identities.

Mapped inflationary symmetry constraints to a 2+1D Euclidean CFT framework.

Highlighted differences between conformal perturbation theory and slow roll expansion.

Abstract

We investigate the symmetry constraints on the bispectrum, i.e. the three-point correlation function 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.