Galaxy Bispectrum from Massive Spinning Particles

TL;DR

The paper develops a general bispectrum template for primordial non-Gaussianity sourced by massive spinning particles during inflation and validates it against full calculations. It then uses a Fisher forecast to assess EUCLID and DESI's ability to constrain the corresponding $f_{NL}$ and mass parameter ν by modeling the galaxy bispectrum in redshift space with tree-level perturbation theory, including RSD and Alcock-Paczynski effects. The results indicate that both surveys could detect $f_{NL}$ around unity for spins 2, 3, and 4, and, if detected, measure the particle masses with tens of percent precision, opening a direct window into the particle content of the early Universe. This work thus provides a concrete pathway to test inflationary physics with the galaxy bispectrum and highlights the importance of accounting for theoretical errors and non-Gaussian covariances in such forecasts.

Abstract

Massive spinning particles, if present during inflation, lead to a distinctive bispectrum of primordial perturbations, the shape and amplitude of which depend on the masses and spins of the extra particles. This signal, in turn, leaves an imprint in the statistical distribution of galaxies; in particular, as a non-vanishing galaxy bispectrum, which can be used to probe the masses and spins of these particles. In this paper, we present for the first time a new theoretical template for the bispectrum generated by massive spinning particles, valid for a general triangle configuration. We then proceed to perform a Fisher-matrix forecast to assess the potential of two next-generation spectroscopic galaxy surveys, EUCLID and DESI, to constrain the primordial non-Gaussianity sourced by these extra particles. We model the galaxy bispectrum using tree-level perturbation theory, accounting for redshift-space distortions and the Alcock-Paczynski effect, and forecast constraints on the primordial non-Gaussianity parameters marginalizing over all relevant biases and cosmological parameters. Our results suggest that these surveys would potentially be sensitive to any primordial non-Gaussianity with an amplitude larger than $f_{\rm NL}\approx 1$, for massive particles with spins 2, 3, and 4. Interestingly, if non-Gaussianities are present at that level, these surveys will be able to infer the masses of these spinning particles to within tens of percent. If detected, this would provide a very clear window into the particle content of our Universe during inflation.

Figures (11)

• Figure 1: Bispectrum due to the exchange of a massive spin-2 particle as function of the momentum ratio for $\nu=3$ (left) and $\nu=6$ (right). The solid and dashed lines correspond to the numerical result and analytical template, respectively.
• Figure 2: Bispectrum due to the exchange of a massive spin-2 particle as a function of the momentum ratio for different permutations. The solid (black), dotted (blue), and dashed (red) lines correspond to the numerical result, analytical template with and without the higher-derivative terms, respectively. The left and right plots correspond to the diagrams $I_1$ and $I_3$ in Eq. \ref{['eq:diagram']}, respectively.
• Figure 3: Analytic shape functions for spin 2 (left) and spin 4 (right) as a function of the base angle $\theta=\cos^{-1}(\hat{{\bf k}}_1\cdot \hat{{\bf k}}_3)$ for fixed ratios of $r=k_1/k_2$. The black curve shows the pure Legendre behavior, whereas the solid, dashed, and dotted colored curves represent the angular dependence when $r= 0.1$, 0.5, and 1, respectively. For easier comparison, each curve has been normalized with respect to the Legendre polynomials.
• Figure 4: Shape correlation between the local \ref{['Blocal']}, equilateral \ref{['Beq']}, quasi-single-field \ref{['BQSF']} non-Gaussianity, and the bispectrum template \ref{['eq:Bfull']} for $s=\{2,3,4\}$ and $\nu=\{3,6\}$.
• Figure 5: Normalized redshift distribution of galaxies for DESI Aghamousa:2016zmz (left) and EUCLID spectroscopic survey Geach:2009tm (right). For DESI, the distribution corresponds to the sum of ELG and LRG galaxies. For EUCLID, the distribution is obtained from empirical data of the luminosity function of H$\alpha$ emitters out to $z=2$. We take the limiting flux to be $4\times 10^{-16} {\rm erg \ s}^ {-1} {\rm cm}^{-2}$ and an efficiency of $35\%$.