Abstract
We study the imprint of higher spin supermultiplets on cosmological correlators, namely the non-Gaussianity of the cosmic microwave background. Supersymmetry is used as a guide to introduce the contribution of fermionic higher spin particles, which have been neglected thus far in the literature. This necessarily introduces more than just a single additional fermionic superpartner, since the spectrum of massive, higher spin super- multiplets includes two propagating higher spin bosons and two propagating higher spin fermions, which all contribute to the three point function. As an example we consider the half-integer superspin Y = s + 1/2 supermultiplet, which includes particles of spin values j = s + 1, j = s + 1/2, j = s + 1/2 and j = s. We compute the curvature perturbation 3-point function for higher spin particle exchange and find that the known Ps(cos θ) angu- lar dependence is accompanied by superpartner contributions that scale as Ps+1(cos θ) and \( {\sum}_m{P}_s^m\left(\cos \theta \right) \), with Ps and \( {P}_s^m \) defined as the Legendre and Associated Legendre polynomials respectively. We also compute the tensor-scalar-scalar 3-point function, and find a complicated angular dependence as an integral over products of Legendre and associated Legendre polynomials.
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Alexander, S., James Gates, S., Jenks, L. et al. Higher spin supersymmetry at the cosmological collider: sculpting SUSY rilles in the CMB. J. High Energ. Phys. 2019, 156 (2019). https://doi.org/10.1007/JHEP10(2019)156
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DOI: https://doi.org/10.1007/JHEP10(2019)156