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

TL;DR

This work investigates how higher-spin supermultiplets, organized by supersymmetry, imprint distinctive angular patterns in the CMB non-Gaussianity via cosmological collider physics. By coupling a higher-spin sector to inflation within a de Sitter–SUSY–EFT framework and evaluating in-in correlators, the authors show that HS boson exchange yields a $P_s(cos\theta)$ pattern while HS fermions contribute additional terms in the form of associated Legendre polynomials $P_s^m(cos\theta)$, with a combined signal emerging from the half-integer superspin multiplet that also includes a $P_{s+1}(cos\theta)$ piece. The resulting HS-SUSY signature is a characteristic angular triad: $P_{s+1}$, a tower of $P_s^m$, and $P_s$, with amplitudes set by SUSY-motivated couplings and Boltzmann suppressions, typically yielding $f_{NL}$ of order unity or smaller. The findings motivate near-future observational searches and point to the need for a full HS de Sitter supergravity framework to fully realize the cosmological collider potential of higher-spin supersymmetry.

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 $P_{s}(\cos θ)$ angular dependence is accompanied by superpartner contributions that scale as $P_{s+1}(\cos θ)$ and $\sum_{m}P^{m}_{s} (\cos θ)$, 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.

Figures (2)

• Figure 1: In-In formalism Feynman Diagrams for exchange of a single higher spin particle.
• Figure 2: Diagram contributing to $\langle \gamma\zeta\zeta \rangle$.