Consistency Relations for the Conformal Mechanism

TL;DR

This paper derives consistency relations for theories with broken conformal symmetry, linking correlation functions and exploring their implications for early universe density perturbations and observable signatures.

Contribution

It systematically establishes new consistency relations for non-linearly realized conformal symmetries with implications for cosmological models.

Findings

Derived identities relate (N+1)-point and N-point functions with a soft Goldstone mode.

Identified a novel one-loop contribution to the four-point function affecting cosmological observations.

Discussed implications for stochastic bias and CMB mu-distortion measurements.

Abstract

We systematically derive the consistency relations associated to the non-linearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearly-realized de Sitter subalgebra. These identities relate (N+1)-point correlation functions with a soft external Goldstone to N-point functions. These relations have direct implications for the recently proposed conformal mechanism for generating density perturbations in the early universe. We study the observational consequences, in particular a novel one-loop contribution to the four-point function, relevant for the stochastic scale-dependent bias and CMB mu-distortion.