# Higher spin supersymmetry at the cosmological collider: sculpting SUSY rilles in the CMB

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## 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 *P*_{s+1}(cos *θ*) and \( {\sum}_m{P}_s^m\left(\cos \theta \right) \), with *P*_{s} 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.

## Keywords

Cosmology of Theories beyond the SM Higher Spin Symmetry Supersym- metric Effective Theories## Notes

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