Halo clustering and g_{NL}-type primordial non-Gaussianity

TL;DR

This work analyzes halo clustering under local-type primordial non-Gaussianity with a cubic term, $\Phi({\bf x})=\Phi_G({\bf x})+g_{NL}(\Phi_G^3-3\langle\Phi_G^2\rangle\Phi_G)$, by combining peak-background split and barrier-crossing formalisms. It derives a simple scale-dependent halo bias $b(k)=b_1+\beta_g g_{NL}/\alpha(k)$ and shows how $\beta_g$ relates to the halo mass function in an $f_{NL}$ cosmology; the authors provide both weak (theoretical) and strong (Edgeworth-based) predictions, and validate these against $N$-body simulations. A refined, universal fitting formula for $\beta_g$ as a function of Gaussian bias $b_1$ and redshift $z$ is proposed, with separate forms for narrow-mass selections and mass-weighted tracer populations. The paper emphasizes that robust $g_{NL}$ constraints from large-scale structure require highly biased tracers ($b_1\gtrsim 2.5$) due to sensitivity to the halo-occupation distribution, and it reconciles analytic approaches with simulations while outlining practical caveats for data analyses.

Abstract

A wide range of multifield inflationary models generate non-Gaussian initial conditions in which the initial adiabatic fluctuation is of the form (zeta_G + g_{NL} zeta_G^3). We study halo clustering in these models using two different analytic methods: the peak-background split framework, and brute force calculation in a barrier crossing model, obtaining agreement between the two. We find a simple, theoretically motivated expression for halo bias which agrees with N-body simulations and can be used to constrain g_{NL} from observations. We discuss practical caveats to constraining g_{NL} using only observable properties of a tracer population, and argue that constraints obtained from populations whose observed bias is <~ 2.5 are generally not robust to uncertainties in modeling the halo occupation distribution of the population.

Figures (3)

• Figure 1: An example to illustrate that halo bias in a $g_{NL}$ cosmology takes the functional form form $b(k) = b_1 + \beta_g g_{NL}/\alpha(k)$. This figure corresponds to redshift $z=0.5$ and halo mass range $1.15 \le M \le 1.83 \times 10^{14}$$h^{-1}$$M_\odot$, but we find the same functional form for all redshifts and halo masses.
• Figure 2: Comparison of the "weak" and "strong" predictions for the scale-dependent bias in a $g_{NL}$ cosmology. Blue squares: Direct estimates of the bias, extracted from simulations with $g_{NL} = \pm 2 \times 10^6$ as described in §\ref{['ssec:bias_fits']}. Green circles: "Weak" analytic prediction for the bias ($\beta_g = 3(\partial\log n/\partial f_{NL})$) from the peak-background split formalism, showing perfect agreement. The estimates of $(\partial\log n/\partial f_{NL})$ shown in the figure were obtained directly from simulations with $f_{NL}=\pm 250$. Red dotted curve: Edgeworth prediction for the bias (Eq. (\ref{['eq:barrier_b2']})). Good agreement is seen at high mass, but at low masses Edgeworth underpredicts $3(d\log n/df_{NL})$. We will find an improvement in §\ref{['ssec:bias_final']}.
• Figure 3: Scale-dependent $g_{NL}$ bias coefficient $\beta_g$ as a function of redshift $z$ and halo bias $b_1$, showing excellent agreement between our final analytic result (Eq. (\ref{['eq:b2_final']}), dashed curves) and $N$-body simulations (error bars).