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 ${g}_{\mathrm{NL}}$. We show that a strong scale dependence in the bias can be produced by ${g}_{\mathrm{NL}}$ of order ${10}^{5}$, consistent with cosmic microwave background constraints. On a separation length of $\ensuremath{\sim}100\text{ }\text{ }\mathrm{Mpc}$, current constraints on ${g}_{\mathrm{NL}}$ 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 ${g}_{\mathrm{NL}}$. We explain why the Edgeworth formalism, though technically challenging, is a very powerful technique for constraining high-order non-Gaussianity with large-scale structures.