Scale-dependent Bias from the Reconstruction of Non-Gaussian Distributions
Abstract
Primordial non-Gaussianity introduces a scale-dependent variation in the clustering of density peaks corresponding to rare objects. This variation, parametrized by the bias, is investigated on scales where a linear perturbation theory is sufficiently accurate. The bias is obtained directly in real space by comparing the one- and two-point probability distributions of density fluctuations. We show that these distributions can be reconstructed using a bivariate Edgeworth series, presented here up to an arbitrarily high order. The Edgeworth formalism is shown to be well-suited for 'local' cubic-order non-Gaussianity parametrized by gNL. We show that a strong scale-dependence in the bias can be produced by gNL of order 10,000, consistent with CMB constraints. On correlation length of ~100 Mpc, current constraints on gNL still allow the bias for the most massive clusters to be enhanced by 20-30% of the Gaussian value. We further examine the bias as a function of mass scale, and also explore the relationship between the clustering and the abundance of massive clusters in the presence of gNL. We explain why the Edgeworth formalism, though technically challenging, is a very powerful technique for constraining high-order non-Gaussianity with large-scale structures.