The Void Abundance with Non-Gaussian Primordial Perturbations

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 f eq nl . 30, over distance scales ∼ 10 Mpc.