Massive Spinning Fields During Inflation: Feynman rules and correlator comparison

TL;DR

This work establishes a detailed comparison between two descriptions of massive spinning fields during inflation: the cosmological collider (CC), which preserves full de Sitter symmetry, and the cosmological condensed matter (CCM) approach, which realizes only the $SO(3)$ subgroup on FRW slices. By deriving Feynman rules for exchange diagrams in both formalisms, the authors uncover mixed propagators and delta-function corrections that encode instantaneous propagation of non-dynamical modes in CC. They show that inflaton bispectrum signals are universal across CC and CCM when restricted to single-helicity exchanges (the bispectrum being dominated by helicity-0 modes in CC tree-level diagrams), while trispectrum and higher-point correlators exhibit genuine nonlocality in the CCM description and cannot be reproduced by any local CCM theory. The results imply that cosmological collider signals in the bispectrum are robust to the detailed description of the heavy spinning field, while higher-point observables can distinguish CC from CCM, with EFToI constraints preserved in the correspondence. This framework paves the way for targeted observational tests and highlights the importance of considering nonlocal effects when matching CC and CCM descriptions beyond the bispectrum.

Abstract

We consider the dynamics of massive spinning fields during inflation and the resulting signatures in the cosmological correlators of inflaton perturbations computed in the Poincaré patch of de Sitter space. There are (at least) two ways to describe the fluctuations of such new spinning degrees of freedom and these are distinguished by the symmetries of the de Sitter group that they linearly realise. The primary question we ask is: do these two set-ups yield distinct signatures in cosmological observables? After systematically deriving the Feynman rules for exchange diagrams consisting of massive spinning fields, where we discover the necessity of effective propagators that augment the naive Schwinger-Keldysh ones by delta functions corresponding to instantaneous propagation, we show that the two set-ups are indistinguishable at the level of the inflaton bispectrum but distinguishable at the level of the trispectrum and other higher-point correlation functions. The bispectrum is special since in the corresponding tree-level Feynman diagrams, only the helicity-zero modes of the spinning fields can propagate. The bispectrum correspondence holds up to the addition of contact diagrams arising from the self-interactions of the inflaton, and is consistent with the symmetries of the effective field theory of inflation. Our results suggest that the cosmological collider signals in the bispectrum are universal and do not depend on the detailed description of the massive spinning field.