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

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 parityodd 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.

Colliding Ghosts: Constraining Inflation with the Parity-Odd Galaxy Four-Point Function

“…In this section we introduce two candidate models for parity-violating inflation: the Ghost Condensate [38,39] and the Cosmological Collider [7,31,57,58,[65][66][67][68][69][70][71][72]. This follows from [37], which studied these two scenarios as examples of models that evade general theorems about parity violation in the scalar sector, and can give rise to a parity-odd trispectrum for the comoving curvature perturbation ζ.…”

“…To understand inflationary parity-violation, we can once again look to the EFTI. Assuming a scale-invariant Universe with a Bunch-Davies vacuum, populated by a set of arbitrary scalar fields (with interactions that fall off sufficiently fast as the modes are stretched outside the horizon during inflation), the parity-odd primordial trispectrum vanishes at tree level [31,37]. Any significant detection would thus indicate violation of one of the above assumptions, and could hint at a variety of non-standard inflationary scenarios.…”

“…Any significant detection would thus indicate violation of one of the above assumptions, and could hint at a variety of non-standard inflationary scenarios. Intriguing examples of this include non-standard vacua such as ghost condensation [38,39], (strong) violation of scale invariance, or the exchange of massive spinning particles [31,37]. As for the bispectrum, each scenario arises from specific terms in the EFTI Lagrangian, whose signatures can be searched for in late-time observables.…”

“…Through their dependence on chiral gravitational waves, these can have parity-sensitive power spectra, for instance, the CMB T B correlator. In contrast, the second class of observables, including CMB T -and E-modes and LSS density fields, depend only on inflationary scalars, thus parity-sensitivity appears only in the trispectrum and beyond (since a parity transformation is equivalent to a rotation for the power spectrum and bispectrum) [29,37,51,52]. In this work, we consider the latter case, noting that the physical origins of scalar-and tensor-type parity violation can be distinct, and there has been no robust detection of gravitational wave signatures to date.…”

“…Indeed, no evidence was found for this model in the former work. Here, we consider two types of parity-breaking motivated by the EFTI and for which the theoretical prediction is under perturbative control: Ghost Inflation [38] and the exchange of a spin-1 particle (part of the Cosmological Collider setup, [e.g., 7, 57, 58]), following the derivations of [37]. In particular, we will place constraints on the corresponding inflationary couplings, and additionally assess whether these scenarios could be responsible for the observed parity-excess.…”