The Void Abundance with Non-Gaussian Primordial Perturbations

TL;DR

The paper investigates how primordial non-Gaussianity affects the abundance of voids in large-scale structure by adapting a PS-like framework to underdensities. It shows that the void population depends on the skewness $S_3$, which encodes $f_{nl}$ for local and equilateral bispectra, and provides forecasts for detectability in future surveys. The authors find that upcoming surveys could probe $f_{nl}$ values as small as $≈10$ for the local model and $≈30$ for the equilateral model, making void counts a competitive, complementary probe to CMB and cluster measurements. They also discuss model dependence, scale dependence, and the need for higher-fidelity simulations to robustly exploit void statistics for non-Gaussianity tests.

Abstract

We use a Press-Schechter-like calculation to study how the abundance of voids changes in models with non-Gaussian initial conditions. While a positive skewness increases the cluster abundance, a negative skewness does the same for the void abundance. We determine the dependence of the void abundance on the non-Gaussianity parameter fnl for the local-model bispectrum-which approximates the bispectrum in some multi-field inflation models-and for the equilateral bispectrum, which approximates the bispectrum in e.g. string-inspired DBI models of inflation. We show that the void abundance in large-scale-structure surveys currently being considered should probe values as small as fnl < 10 and fnl^eq < 30, over distance scales ~10 Mpc.

Figures (3)

• Figure 1: Skewness $S_{3,R}$ for a non-Gaussianity parameter $f_{\mathrm{nl}}=1$ as function of radius $R$. The dashed line is the local non-Gaussian model; the solid line is the equilateral model; and the dotted line is the DBI-type equilateral model for a scale-dependence parameter $\kappa=-0.3$. See Ref. LoVerde:2007ri for details. We also indicate the scales probed by halo and void abundances.
• Figure 2: The ratio of the void abundance with non-Gaussianity at the level of $|f_{\mathrm{nl}}|=30$ to the void abundance with Gaussian initial conditions as a function of the void size $R$. The curves are evaluated for a central redshift $z=0.8$, and the points are $1\sigma$ Poisson errors for a survey of width $\Delta z=0.3$ that covers 30,000 square degrees for a fiducial Gaussian case. The curve with a large ratio at large $R$ is for $f_{\mathrm{nl}}<0$, while the curve with the small ratio at large $R$ is for $f_{\mathrm{nl}}>0$.
• Figure 3: The smallest local-model $f_{\mathrm{nl}}$ detectable at the $1\sigma$ level, as a function of the critical underdensity $\delta_v$, for several surveys currently under study. The solid upper line is for something like the BOSS SDSS-3 survey using the void-size distribution over the range $2~h^{-1}~{\mathrm{Mpc}}< R <60~h^{-1}~{\mathrm{Mpc}}$. The lower two (dashed) curves are for an ADEPT-like survey. The upper dashed curve uses only the void distribution with $R>8\,h^{-1}~{\mathrm{Mpc}}$; the lower dashed curve uses $2~h^{-1}\,{\mathrm{Mpc}}> R< 60~h^{-1}\, {\mathrm{Mpc}}$.