The structure of correlation functions in single field inflation

TL;DR

This paper investigates the structure of correlation functions in single-field inflation models with higher derivatives, focusing on conditions for Gaussian expansion and the impact of sound speed on non-Gaussianity.

Contribution

It formalizes the conditions under which inflationary fluctuations can be approximated as Gaussian, especially in models with higher derivative interactions and varying sound speed.

Findings

Correlation functions can deviate from hierarchical scaling in models with significant non-Gaussianity.

The sound speed influences the scaling behavior of correlation functions.

Special considerations are discussed for Dirac-Born-Infeld inflation.

Abstract

Many statistics available to constrain non-Gaussianity from inflation are simplest to use under the assumption that the curvature correlation functions are hierarchical. That is, if the n-point function is proportional to the (n-1) power of the two-point function amplitude and the fluctuations are small, the probability distribution can be approximated by expanding around a Gaussian in moments. However, single-field inflation with higher derivative interactions has a second small number, the sound speed, that appears in the problem when non-Gaussianity is significant and changes the scaling of correlation functions. Here we examine the structure of correlation functions in the most general single scalar field action with higher derivatives, formalizing the conditions under which the fluctuations can be expanded around a Gaussian distribution. We comment about the special case of the Dirac-Born-Infeld action.