Signature of primordial non-Gaussianity of phi^3-type in the mass function and bias of dark matter haloes

TL;DR

This study investigates local cubic primordial non-Gaussianity through the cubic coupling g_NL in the relation Phi = phi + g_NL phi^3 and its impact on the halo mass function and large-scale bias using large N-body simulations. The authors develop and test analytic forms for non-Gaussian corrections to both the halo mass function and the bias, finding good agreement for the mass function but a suppressed, not fully predicted, scale-dependent bias that requires empirical corrections (epsilon_kappa, epsilon_I). They quantify current observational constraints on g_NL from large-scale structure and forecast substantial improvements with future surveys and CMB data, highlighting the potential to test curvaton- and multi-field-inspired scenarios. Overall, the work provides a practical framework for incorporating g_NL into halo statistics and demonstrates that forthcoming data could robustly probe cubic-type non-Gaussianity.

Abstract

We explore the effect of a cubic correction gnl*phi^3 on the mass function and bias of dark matter haloes extracted from a series of large N-body simulations and compare it to theoretical predictions. Such cubic terms can be motivated in scenarios like the curvaton model, in which a large cubic correction can be produced while simultaneously keeping the quadratic fnl*phi^2 correction small. The deviation from the Gaussian halo mass function is in reasonable agreement with the theoretical predictions. The scale-dependent bias correction Delta b_kappa(k,gnl) measured from the auto- and cross-power spectrum of haloes, is similar to the correction in fnl models, but the amplitude is lower than theoretical expectations. Using the compilation of LSS data in Slosar et al. (2008), we obtain for the first time a limit on gnl of -3.5*10^5 < gnl < +8.2*10^5 (at 95% CL). This limit will improve with the future LSS data by 1-2 orders of magnitude, which should test many of the scenarios of this type.

Figures (11)

• Figure 1: Skewness and kurtosis of the initial ($z=99$) density field as a function of smoothing radius. While the top panel shows the sum of the contributions arising from the Zel'dovich dynamics and from primordial non-Gaussianity, $S_3=S_3^{\rm Zel}+S_3^{\rm Pri}$, the bottom panel only shows the absolute value of the primordial kurtosis, $|S_4^{\rm Pri}|$. Symbols represent the numerical results averaged over the realisations. They have been slightly shifted horizontally for clarity. Error bars show the scatter among the realisations for the models with $g_{\rm NL}=10^6$. Solid lines indicate the theoretical expectations.
• Figure 2: Non-Gaussian fractional correction $\beta_{\rm m}(k,g_{\rm NL})=P_{\rm mm}(k,g_{\rm NL})/P_{\rm mm}(k,0)-1$ to the matter power spectrum after subtracting a scale-independent normalisation shift $6g_{\rm NL}\langle\phi^2\rangle$ induced by the cubic coupling $g_{\rm NL}\phi^3$.
• Figure 3: Variance $\sigma$ (dotted), skewness $\sigma S_3^{(1)}$ (dashed) and kurtosis $\sigma^2 S_4^{(1)}$ (solid) of the smoothed linear density field $\delta_M$ as a function of mass scale $M$.
• Figure 4: Top panel : Fractional correction to the Gaussian multiplicity function of dark matter haloes as a function of the peak height $\nu(M,z)$ for a coupling parameter $g_{\rm NL}=\pm 10^6$. The dotted, dashed and solid curves show the theoretical predictions eqs. (\ref{['eq:loverde']}), (\ref{['eq:mvj']}) and (\ref{['eq:thiswork']}) at $z=0$, respectively. Error bars denote Poisson errors. For illustration, $M=10^{15}\ {\rm M_\odot/{\it h}}$ corresponds to $\nu=3.2$, 5.2, 7.7 at redshift $z=0$, 1 and 2, respectively. Similarly, $M=10^{14}\ {\rm M_\odot/{\it h}}$ and $10^{13}\ {\rm M_\odot/{\it h}}$ correspond to $\nu=1.9$, 3, 4.5 and 1.2, 1.9, 2.9 respectively. Bottom panel : a comparison with equation (\ref{['eq:thiswork']}) evaluated at $z=0$ and 2.
• Figure 5: Top panel : Non-Gaussian bias correction computed from the halo-matter power spectrum of haloes of mass $M>2\times 10^{13}\ {\rm M_\odot/{\it h}}$ extracted from the snapshot at $z=0.5$ (filled symbols). The solid curve represents $P_{\rm mh}(k,g_{\rm NL})/P_{\rm mh}(k,0)-1$ with a non-Gaussian bias shift $\Delta b(k,g_{\rm NL})$ given by Eq. (\ref{['eq:dbias']}). The dashed, dotted and dotted-dashed curves show three separate contributions that arise at first order in $g_{\rm NL}$. Bottom panel : $\Delta b(k,g_{\rm NL})$ is replaced by the theoretical model Eq. (\ref{['eq:dbiaseff']}). The shaded region indicates the data points used to fit the parameters $\epsilon_\kappa$ and $\epsilon_{\rm I}$. Error bars indicate the scatter among 5 realisations.