Interactions of partially massless spin-2 with spin-3/2 fields are obstructed at second order unless a massless graviton is added, leading to N=1 conformal supergravity.
Imprints of Spinning Particles on Primordial Cosmological Perturbations
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If there exist higher-spin particles during inflation which are light compared to the Hubble rate, they may leave distinct statistical anisotropic imprints on the correlators involving scalar and graviton fluctuations. We characterise such signatures using the dS/CFT$_3$ correspondence and the operator product expansion techniques. In particular, we obtain generic results for the case of partially massless higher-spin states.
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A note on partially massless supergravity
Interactions of partially massless spin-2 with spin-3/2 fields are obstructed at second order unless a massless graviton is added, leading to N=1 conformal supergravity.