A Naturally Large Four-Point Function in Single Field Inflation

TL;DR

This paper demonstrates that certain natural single-field inflation models can produce a large four-point non-Gaussianity, which is usually subdominant, by imposing symmetries that suppress the three-point function.

Contribution

It introduces models with symmetries that naturally enhance the four-point function in single-field inflation, providing a unique shape for the non-Gaussianity.

Findings

Large four-point function can dominate non-Gaussianity in specific models.

Imposing symmetries suppresses the three-point function, making the four-point signal prominent.

Unique shape of the four-point function is derived for certain dispersion relations.

Abstract

Non-Gaussianities of the primordial density perturbations have emerged as a very powerful possible signal to test the dynamics that drove the period of inflation. While in general the most sensitive observable is the three-point function in this paper we show that there are technically natural inflationary models where the leading source of non-Gaussianity is the four-point function. Using the recently developed Effective Field Theory of Inflation, we are able to show that it is possible to impose an approximate parity symmetry and an approximate continuos shift symmetry on the inflaton fluctuations that allow, when the dispersion relation is of the form $\omega\sim c_s k$, for a unique quartic operator, while approximately forbidding all the cubic ones. The resulting shape for the four-point function is unique. In the models where the dispersion relation is of the form $\omega\sim k^2/M$ a similar construction can be carried out and additional shapes are possible.