General Spin-1 Dynamics During Inflation: Microcausality Constraints and Cosmological Collider Signals

Abstract

We construct the general theory of a spin-1 field propagating on an inflationary background consistent with scale invariance, rotations, Bunch-Davies conditions and microcausality. Our Boostless Proca theory generalises the usual massive Proca theory to a Lagrangian with 5 free parameters: 4 corresponding to parity-even terms and a single parity-odd term. We impose three degrees of freedom from the outset and find that microcausality, the statement that field operators vanish outside the lightcone, requires the kinetic terms to be gauge invariant. We couple this spin-1 state to the inflaton and study the signatures it imprints on cosmological correlators. We find no new signals for the bispectrum meaning that the known signals are the most general thereby providing a very clean model-independent probe of new physics in this leading form of non-Gaussianity. For the trispectrum and higher-point functions, the boostless Proca theory produces new shapes with all 5 parameters in principle measurable.