Consequences of a stochastic approach to the conformal invariance of inflationary correlators

TL;DR

This paper develops a stochastic formalism to compute infrared correlators of multiple scalar fields in de Sitter space, revealing complex structures and conditions for conformal invariance that impact inflationary models.

Contribution

It introduces a general stochastic approach to calculate scalar field correlators in de Sitter space, clarifying conditions for conformal invariance and scaling behavior.

Findings

Derived the form and amplitude of three-point functions from conformal invariance.

Identified conditions under which correlators obey naive scaling.

Showed that correlation functions can have more complex structures than previously thought.

Abstract

We provide a general formalism to calculate the infrared correlators of multiple interacting scalar fields in the de Sitter space by means of the stochastic approach. These scalar fields are treated as test fields and hence our result is applicable to the models such as the curvaton scenario where the fields that yield initially isocurvature modes do not contribute to the cosmic energy density during inflationary expansion. The stochastic formalism combined with the argument of conformal invariance of the correlators reflecting the de Sitter isometries allows us to fix the form and amplitude of the three-point functions completely and partially for the four-point functions in terms of calculable quantities. It turns out that naive scaling argument employed in the previous literature does not necessarily hold and we derive the necessary and sufficient condition for the correlator to obey the naive scaling. We also find that correlation functions can in principle exhibit more complicated structure than argued in the literature.