Partially Massless Fields During Inflation

TL;DR

This work investigates partially massless (PM) fields in de Sitter space and their possible role during inflation. By constructing gauge-invariant couplings between PM higher-spin fields and inflationary perturbations, the authors compute distinct signatures in cosmological correlators using in-in techniques and soft-limit analyses. They find that PM exchanges can strictly violate the tensor consistency relation in the tensor-scalar-scalar bispectrum while leaving the scalar bispectrum vanishing, and that PM fields enhance the collapsed limit of the scalar trispectrum without generating a scalar trispectrum in other configurations. These unique soft-limit signatures provide clean observational channels to detect PM fields during inflation and to test the de Sitter-like nature of the inflationary epoch, with implications for high-spin dynamics in curved spacetime.

Abstract

The representation theory of de Sitter space allows for a category of partially massless particles which have no flat space analog, but could have existed during inflation. We study the couplings of these exotic particles to inflationary perturbations and determine the resulting signatures in cosmological correlators. When inflationary perturbations interact through the exchange of these fields, their correlation functions inherit scalings that cannot be mimicked by extra massive fields. We discuss in detail the squeezed limit of the tensor-scalar-scalar bispectrum, and show that certain partially massless fields can violate the tensor consistency relation of single-field inflation. We also consider the collapsed limit of the scalar trispectrum, and find that the exchange of partially massless fields enhances its magnitude, while giving no contribution to the scalar bispectrum. These characteristic signatures provide clean detection channels for partially massless fields during inflation.

Figures (5)

• Figure 1: Spectrum of spin-0 (top) and spin-4 fields (bottom) in de Sitter space. The green points correspond to masses in the discrete series.
• Figure 2: Tree-level diagrams contributing to $\langle\gamma\zeta\zeta\rangle$ (left) and $\langle\zeta\zeta\zeta\zeta\rangle$ (right).
• Figure 3: Angular dependence $\hat{Y}^2_s(\theta,0)+\hat{Y}^{-2}_s(\theta,0)$ due to the exchange of a depth-1 partially massless field as a function of the angle $\theta=\cos^{-1}(\hat{{\bf k}}_1\cdot\hat{{\bf k}}_3)$. The solid, dashed, and dotted lines correspond to spins 4, 6, and 8, respectively.
• Figure 4: Sketch of the trispectrum in the collapsed configuration. The information on the spin of the exchanged (partially) massless field is contained in the $(\theta,\theta',\psi)$ dependence of the trispectrum.
• Figure 5: Schematic illustration of current and future constraints on the scalar trispectrum (top) Cooray:2008ebYamauchi:2015mjaBartolo:2015fqzAde:2015ava and tensor-scalar-scalar bispectrum (bottom) Shiraishi:2010kdMeerburg:2016ecvAbazajian:2016yjjShiraishi:2017yrq for local non-Gaussianity. The red and green regions correspond to the sensitivity levels of Planck Ade:2015ava and forthcoming experiments, respectively. The "gravitational floor" refers to the guaranteed level of non-Gaussianity sourced by gravitational nonlinearities during inflation, while "non-perturbative" denotes the strongly non-Gaussian regime.