The void abundance with non-gaussian primordial perturbations

Abstract

We use a Press-Schechter-like calculation to study how theabundance of voids changes in models with non-Gaussian initialconditions. While a positive skewness increases the cluster abundance, a negative skewness does thesame for the void abundance. We determine the dependence of thevoid abundance on the non-Gaussianity parameter fnl for thelocal-model bispectrum—which approximates the bispectrum insome multi-field inflation models—and for the equilateralbispectrum, which approximates the bispectrum in single-fieldslow-roll inflation and in string-inspired DBI models ofinflation. We show that the void abundance inlarge-scale-structure surveys currently being considered shouldprobe values as small as fnl ≲ 10 andfnleq ≲ 30, over distance scales ∼ 10 Mpc.