Detecting higher spin fields through statistical anisotropy in the CMB bispectrum

TL;DR

This work investigates how long-lived higher-spin fields during inflation can imprint statistical anisotropy in the CMB bispectrum. By deriving the angular dependence of the primordial curvature bispectrum and decomposing it into Legendre components, it provides explicit expressions for the coefficients $c_n$ in both partially massless and other higher-spin scenarios (including spin-3 and spin-4 cases). It then projects these signals onto the CMB, computes angle-averaged bispectra, and performs Fisher forecasts under a cosmic-variance-limited assumption, finding that the errors on $c_n$ scale as $\Delta c_n \propto \ell_{\max}^{-1}$ and grow approximately as $n^2$, with potential detectability of even coefficients (e.g., $c_2$ around 10). The results suggest that next-generation CMB data, and possibly LSS or 21-cm surveys, could constrain or detect higher-spin-induced anisotropies, providing a novel window into inflationary particle content and dS/CFT-inspired predictions.

Abstract

Inflation may provide a suitable collider to probe physics at very high energies. In this paper we investigate the impact on the CMB bispectrum of higher spin fields which are long-lived on super-Hubble scales, e.g. partially massless higher spin fields. We show that distinctive statistical anisotropic signals on the CMB three-point correlator are induced and we investigate their detectability.

Figures (5)

• Figure 1: A schematic view of various realizations of the first $N-N_k$ e-folds of inflation where each of the unsuppressed IR super-Hubble higher spin modes $A_{\mu_1 \cdots \mu_s }^{IR}$ behaves as non-trivial background. The cosmological correlators are sensitive to the value the IR modes assume in a single realization of the ensemble of possible universes.
• Figure 2: Intensity distributions of the primordial curvature bispectra ${\cal B}_{k_1 k_2 k_3}^{n= 0, 2, 4, 6, 8, 10}$ in the $k$-space tetrahedral domain, where the axes correspond to $k_1 r_*$, $k_2 r_*$ and $k_3 r_*$, respectively, with $r_*$ the conformal distance from the last-scattering surface. To highlight the dominant configurations, the bispectrum shapes are rescaled using $k_1^{-2} k_2^{-2} k_3^{-2}$. Dense red (blue) color represents larger positive (negative) signal.
• Figure 3: Intensity distributions of the CMB bispectra $b_{\ell_1 \ell_2 \ell_3}^{n= 0, 2, 4, 6, 8, 10}$ in the $\ell$-space tetrahedral domain where the axes correspond to $\ell_1$, $\ell_2$ and $\ell_3$, respectively. For highlighting the dominant configurations, the bispectrum shapes are rescaled using a constant Sachs-Wolfe template Fergusson:2009nv. Dense red (blue) color represents larger positive (negative) signal.
• Figure 4: Expected $1\sigma$ errors on $c_{0, 2, 4, 6, 8, 10}$ as a function of $\ell_{\rm max}$. The solid and dashed lines are computed using the exact expression \ref{['eq:CMB_bis_all']} and the SW formula \ref{['eq:CMB_bis_SW']}, respectively. The results for $n = 2$ are consistent with those obtained in Ref. Shiraishi:2013vja.
• Figure 5: Expected $1\sigma$ errors on $c_{n = \rm even}$ at $\ell_{\rm max} = 100$ and $200$ as a function of $n$. These lines are estimated using the SW formula \ref{['eq:CMB_bis_SW']}.