# Higher Spin Supersymmetry at the Cosmological Collider: Sculpting SUSY Rilles in the CMB

## TL;DR

This paper investigates how higher spin supermultiplets, guided by supersymmetry, influence non-Gaussian features in the CMB, revealing new angular dependencies from fermionic superpartners in cosmological correlators.

## Contribution

It introduces the contribution of fermionic higher spin particles in cosmological correlators, expanding the understanding of supersymmetric effects on the CMB beyond previous scalar-only analyses.

## Key findings

- Derived the angular dependence of the 3-point function with superpartner contributions.
- Identified new Legendre polynomial contributions from fermionic superpartners.
- Computed complex angular structures in tensor-scalar-scalar correlators.

## 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 supermultiplets 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 $\textsf{Y}=s+1/2$ 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 $P_{s}(\cos \theta)$ angular dependence is accompanied by superpartner contributions that scale as $P_{s+1}(\cos \theta)$ and $\sum_{m}P^{m}_{s} (\cos \theta)$, 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.