Scale Dependence of Halo Bispectrum from Non-Gaussian Initial Conditions in Cosmological N-body Simulations

TL;DR

The paper demonstrates that local-type primordial non-Gaussianity imprints a strong, measurable signature on the halo bispectrum, especially for squeezed triangles at large scales. Using large-volume N-body simulations with varying $f_{ m NL}$ and a local bias framework, the study confirms that halo bispectrum amplitudes scale roughly as $f_{ m NL}^2$ and that the dominant non-Gaussian contribution in halos arises from the $B_{ m g}^{(2)}$ (or $B_{ m h}^{(2)}$) term, which has a distinct shape and scale dependence. The results show consistent shape dependence with Jeong & Komatsu perturbation theory and reveal that the effect strengthens for more massive halos and higher redshifts, offering a powerful probe to discriminate inflationary scenarios. Forecasts for future surveys indicate detectable signals even with a limited set of triangle configurations, highlighting the potential of the halo/galaxy bispectrum, including the $f_{ m NL}^2$ term, to tighten constraints on local-type primordial non-Gaussianity in upcoming wide-area, deep datasets.

Abstract

We study the halo bispectrum from non-Gaussian initial conditions. Based on a set of large $N$-body simulations starting from initial density fields with local type non-Gaussianity, we find that the halo bispectrum exhibits a strong dependence on the shape and scale of Fourier space triangles near squeezed configurations at large scales. The amplitude of the halo bispectrum roughly scales as $f_nl^2$. The resultant scaling on the triangular shape is consistent with that predicted by Jeong & Komatsu based on perturbation theory. We systematically investigate this dependence with varying redshifts and halo mass thresholds. It is shown that the $f_nl$ dependence of the halo bispectrum is stronger for more massive haloes at higher redshifts. This feature can be a useful discriminator of inflation scenarios in future deep and wide galaxy redshift surveys.

Figures (10)

• Figure 1: The ratio of the halo mass functions for non-Gaussian and Gaussian initial conditions at $z=0.5$. The symbols show the measurements from our simulations, while the lines are equations (\ref{['eq:mf_l']}) and (\ref{['eq:mf_m']}). The values of $f_{\rm NL}$ are $1000$, $300$, $100$, $0$, $-100$, $-300$, and $-1000$ from top to bottom.
• Figure 2: Fractional differences of the matter power spectra starting from non-Gaussian and Gaussian initial conditions. Symbols show the results of $N$-body simulations, while lines are perturbation theory predictions of equation (\ref{['eq:pow_pt']}) ($f_{\rm NL}=300,100,0,-100, -300$ from top to bottom at $k\hbox{$\; \buildrel > \over \sim \;$}0.02h$Mpc$^{-1}$).
• Figure 3: The power spectrum of haloes more massive than $4.6\times10^{13}h^{-1}M_\odot$ at $z=0.5$. Symbols are results of $N$-body simulations, while lines are theoretical prediction of equation (\ref{['eq:pow_bias']}) with (\ref{['eq:q_grossi']}) where we adopt $q=1.0$ for dotted lines and $q=0.75$ for solid lines ($f_{\rm NL}=300,100,0,-100, -300$ from top to bottom).
• Figure 4: The matter bispectrum. Each panel shows the results for an isosceles configuration specified by $\alpha\equiv k_1/k_3$ and $k\equiv k_1=k_2$. Symbols are measurements from $N$-body simulations (the average and the standard error among different realizations) and solid lines are the perturbation theory predictions of equation (\ref{['eq:bis_pt']}).
• Figure 5: The halo bispectrum for some triangular configurations. Each panel shows the result for an isosceles configuration specified by $\alpha\equiv k_1/k_3$ and $k\equiv k_1=k_2$. Error bars are measurements from our simulations (the average and the standard error among different realizations) and solid lines are their $4$-th order polynomial fits, while we keep the terms up to second and linear order for dashed and dotted lines. We use the outputs at $z=0.5$ and consider the haloes more massive than $4.6\times10^{13}h^{-1}M_\odot$.