The void abundance with non-gaussian primordial perturbations

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 single-field slow-roll inflation and in 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 fnleq ≾ 30, over distance scales ~ 10 Mpc.