Massive Exchange and the Sign of the Equilateral Bispectrum

TL;DR

This paper investigates the conditions under which the inflationary bispectrum, generated by massive scalar exchange, can be positive or negative, revealing that its sign depends on the operator structure in the EFT of inflation.

Contribution

It demonstrates that the sign of the equilateral bispectrum is not universal and depends on the interplay of multiple operators in the EFT, especially when considering multiple particles and sound speed effects.

Findings

The bispectrum is strictly negative with only the leading interaction.

Additional operators can produce a positive bispectrum in the equilateral configuration.

A critical ratio of interaction coefficients determines the sign of the bispectrum.

Abstract

We study the inflationary bispectrum generated by the tree-level exchange of a massive hidden-sector scalar during inflation. When the interaction between the inflaton and the hidden sector arises only from the leading boost-breaking operator of the Effective Field Theory (EFT) of inflation, the equilateral bispectrum for principal-series scalar exchange is known to be universally negative, independent of the sign of the coupling. We revisit this result within the full EFT operator basis. Using bootstrap methods, we construct the de Sitter-invariant seed four-point function and obtain the inflationary bispectrum via weight-shifting operators and a soft-limit procedure. While the equilateral bispectrum remains strictly negative when only the leading interaction is present, additional operators generate independent cubic structures whose contributions compete in the equilateral configuration. As a result, the sign of the bispectrum is no longer universal. We derive a critical ratio of interaction coefficients that separates regions of positive and negative equilateral bispectrum. We further study the effects of reduced sound speed $c_s<1$ and the exchange of multiple particles. In both cases, the critical ratio is modified, and for multi-particle exchange a positive equilateral bispectrum can arise even when the higher-order operator is subdominant. Our results show that the negativity of the equilateral bispectrum from massive exchange is not generic, but reflects a restricted operator structure in the EFT of inflation.