The trispectrum of 21-cm background anisotropies as a probe of primordial non-Gaussianity

TL;DR

This work investigates how the 21-cm background from neutral hydrogen before reionization can probe primordial non-Gaussianity beyond the standard bispectrum. By formulating the angular trispectrum and introducing the three-to-one correlator as a compact statistic, the authors show how the cubic non-Gaussian coupling $f_2$ (also termed $g_{ m NL}$) can be constrained, potentially down to ${ m O}(10)$, across $z\sim 50$–$100$, while discussing separation from nonlinear gravitational evolution. The analysis highlights that, even with Gaussian variance dominating the noise, multi-redshift 21-cm data and optimal filtering could yield meaningful constraints on $f_2$ and test consistency relations like $ au_{ m NL}=(6 f_{ m NL}/5)^2$, especially when combined with bispectrum measurements that bound $f_{ m NL}$ to ~0.1. Foregrounds and instrument noise remain major practical challenges, but the approach offers a powerful, tomographic avenue to study inflationary physics beyond the capabilities of the CMB alone.

Abstract

The 21-cm anisotropies from the neutral hydrogen distribution prior to the era of reionization is a sensitive probe of primordial non-Gaussianity. Unlike the case with cosmic microwave background, 21-cm anisotropies provide multi-redshift information with frequency selection and is not damped at arcminute angular scales. We discuss the angular trispectrum of the 21-cm background anisotropies and discuss how the trispectrum signal generated by the primordial non-Gaussianity can be measured with the three-to-one correlator and the corresponding angular power spectrum. We also discuss the separation of primordial non-Gaussian information in the trispectrum with that generated by the subsequent non-linear gravitational evolution of the density field. While with the angular bispectrum of 21-cm anisotropies one can limit the second order corrections to the primordial fluctuations below f_NL< 1, using the trispectrum information we suggest that the third order coupling term, f_2 or g_NL, can be constrained to be arounde 10 with future 21-cm observations over the redshift interval of 50 to 100.

Figures (2)

• Figure 1: The power spectrum of 21-cm anisotropies (top solid line) and the angular power spectrum of the projected three-to-one correlator described in the paper as a probe of the 21 cm trispectrum. In addition to $X_l^{\rm prim}$ with $f_{\rm NL}=10$ and $f_2=1$, we also show $X_l^{\rm grav}$ and $N_l$.
• Figure 2: Signal-to-noise ratio for a detection of $X_l^{\rm prim}$ with $f_{\rm NL}=10$ and $f_2=3$ (solid line) and $f_{\rm NL}=0$ and $f_2=3$ (dot-dashed line). For reference, we show the signal-to-noise ratio associated with the detection of the full 21-cm bispectrum with a dashed line.