Probing higher-spin fields from inflation with higher-order statistics of the CMB

We investigate the degree to which the Cosmic Microwave Background (CMB) can be used to constrain primordial non-Gaussianity coming from the presence of spinning particles coupled to the inflaton. We compute the $\langle TTT \rangle$ and $\langle TTTT \rangle$ correlation functions arising from the exchange of a particle with spin $s$ and generic mass, and the corresponding signal-to-noise ratios for a cosmic-variance-limited CMB experiment. We show that already with \emph{Planck} data one could improve the theoretical bounds on the amplitude of these primordial templates by an order of magnitude. We particularly emphasize the fact that the trispectrum could be sizable even if the bispectrum is not, making it a prime observable to explore the particle content during inflation.