Non-Gaussian Halo Bias Beyond the Squeezed Limit

TL;DR

This paper extends the understanding of primordial non-Gaussianity's impact on large-scale structure by generalizing the scale-dependent bias beyond the squeezed limit, revealing significant corrections at smaller scales.

Contribution

It provides a generalized framework for scale-dependent bias that applies to smaller scales without assuming tracer specifics, beyond the traditional squeezed limit approximation.

Findings

Standard derivation valid only in the squeezed limit

Generalization to smaller scales without tracer assumptions

Subleading bias term scales as k^{eta+2} and becomes relevant at k >~ 0.01 h Mpc^{-1}

Abstract

Primordial non-Gaussianity, in particular the coupling of modes with widely different wavelengths, can have a strong impact on the large-scale clustering of tracers through a scale-dependent bias with respect to matter. We demonstrate that the standard derivation of this non-Gaussian scale-dependent bias is in general valid only in the extreme squeezed limit of the primordial bispectrum, i.e. for clustering over very large scales. We further show how the treatment can be generalized to describe the scale-dependent bias on smaller scales, without making any assumptions on the nature of tracers apart from a dependence on the small-scale fluctuations within a finite region. If the leading scale-dependent bias \Delta b \propto k^{\alpha}, then the first subleading term will scale as k^{\alpha+2}. This correction typically becomes relevant as one considers clustering over scales k >~ 0.01 h Mpc^{-1}.