Scale-dependent Bias from the Reconstruction of Non-Gaussian Distributions

TL;DR

This paper investigates how primordial non-Gaussianity, especially local cubic-order type, affects the scale-dependent bias in large-scale structure clustering, using an Edgeworth series approach to reconstruct probability distributions.

Contribution

It introduces a method to directly compute bias from probability distributions using a high-order Edgeworth expansion, particularly for local g_NL non-Gaussianity.

Findings

Strong scale-dependent bias can be generated by g_NL of order 10,000.

Current constraints allow a 20-30% enhancement in bias for massive clusters.

Edgeworth formalism effectively constrains high-order non-Gaussianity from large-scale structure data.

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 g_NL. We show that a strong scale-dependence in the bias can be produced by g_NL of order 10,000, consistent with CMB constraints. On correlation length of ~100 Mpc, current constraints on g_NL 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 g_NL. We explain why the Edgeworth formalism, though technically challenging, is a very powerful technique for constraining high-order non-Gaussianity with large-scale structures.