Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation

TL;DR

This paper uses conformal symmetry and Ward identities to relate and constrain the three-point scalar correlator during inflation, showing it is generally suppressed and linked to the four-point function.

Contribution

It derives model-independent Ward identities from conformal invariance that connect the three- and four-point scalar correlators in inflation.

Findings

Three-point function is suppressed, similar to slow roll predictions.

The three-point function is determined by the four-point function up to a suppressed constant.

Ward identities are derived from reparametrization invariance of the universe's wave function.

Abstract

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.