Parity violation in the scalar trispectrum: no-go theorems and yes-go examples

TL;DR

This paper establishes no-go theorems for the parity-odd scalar trispectrum in inflationary models and provides explicit examples where these theorems are violated, highlighting the trispectrum's potential to probe new physics.

Contribution

The paper derives no-go theorems for parity-odd trispectra and presents explicit models where these theorems are bypassed, expanding understanding of parity violation in inflation.

Findings

Parity-odd scalar trispectrum vanishes with multiple scalar fields under certain conditions.

Parity-odd correlators with massless spinning fields vanish in the specified setup.

Explicit examples show violations of no-go theorems when assumptions are relaxed.

Abstract

We derive a set of no-go theorems and yes-go examples for the parity-odd primordial trispectrum of curvature perturbations. We work at tree-level in the decoupling limit of the Effective Field Theory of Inflation and assume scale invariance and a Bunch-Davies vacuum. We show that the parity-odd scalar trispectrum vanishes in the presence of any number of scalar fields with arbitrary mass and any parity-odd scalar correlator vanishes in the presence of any number of spinning fields with massless de Sitter mode functions, in agreement with the findings of Liu, Tong, Wang and Xianyu [1]. The same is true for correlators with an odd number of conformally-coupled external fields. We derive these results using both the (boostless) cosmological bootstrap, in particular the Cosmological Optical Theorem, and explicit perturbative calculations. We then discuss a series of yes-go examples by relaxing the above assumptions one at the time. In particular, we provide explicit results for the parity-odd trispectrum for (i) violations of scale invariance in single-clock inflation, (ii) the modified dispersion relation of the ghost condensate (non-Bunch-Davies vacuum), and (iii) interactions with massive spinning fields. Our results establish the parity-odd trispectrum as an exceptionally sensitive probe of new physics beyond vanilla inflation.