Non-Gaussian bias: insights from discrete density peaks

Abstract

Corrections induced by primordial non-Gaussianity to the linear halo bias can be computed from a peak-background split or the widespread local bias model. However, numerical simulations clearly support the prediction of the former, in which the non-Gaussian amplitude is proportional to the linear halo bias. To understand better the reasons behind the failure of standard Lagrangian local bias, in which the halo overdensity is a function of the local mass overdensity only, we explore the effect of a primordial bispectrum on the 2-point correlation of discrete density peaks. We show that the effective local bias expansion to peak clustering vastly simplifies the calculation. We generalize this approach to excursion set peaks and demonstrate that the resulting non-Gaussian amplitude, which is a weighted sum of quadratic bias factors, precisely agrees with the peak-background split expectation, which is a logarithmic derivative of the halo mass function with respect to the normalisation amplitude. We point out that statistics of thresholded regions can be computed using the same formalism. Our results suggest that halo clustering statistics can be modelled consistently (in the sense that the Gaussian and non-Gaussian bias factors agree with peak-background split expectations) from a Lagrangian bias relation only if the latter is specified as a set of constraints imposed on the linear density field. This is clearly not the case of standard Lagrangian local bias. Therefore, one is led to consider additional variables beyond the local mass overdensity.

24 pages. no figure (v2): minor clarification added. submitted to JCAP (v3): 1 figure added. in Press in JCAP

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• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Lagrangian bias of generic large-scale structure tracers
• Measuring nonlocal Lagrangian peak bias
• Impacts of biasing schemes in the one-loop integrated perturbation theory
• The statistics of peaks of weakly non-Gaussian random fields: Effects of bispectrum in two- and three-dimensions
• Tidal shear and the consistency of microscopic Lagrangian halo approaches
• Scale-dependent bias from an inflationary bispectrum: the effect of a stochastic moving barrier
• Symmetries, Invariants and Generating Functions: Higher-order Statistics of Biased Tracers