Deriving an Accurate Formula of Scale-dependent Bias with Primordial Non-Gaussianity: An Application of the Integrated Perturbation Theory

TL;DR

This paper develops a comprehensive framework using integrated perturbation theory to accurately derive the scale-dependent bias caused by primordial non-Gaussianity, including effects of redshift-space distortions, and clarifies the dependence on primordial bispectrum and bias models.

Contribution

It introduces a general formula for scale-dependent bias incorporating various bias models and redshift-space distortions, extending previous formulas derived under specific approximations.

Findings

The slope of large-scale scale-dependent bias depends only on the primordial bispectrum in the squeezed limit.

The amplitude of the bias is sensitive to the bias model used.

Redshift-space distortions have minimal impact on the monopole component but affect the quadrupole component.

Abstract

We apply the integrated perturbation theory (Matsubara 2011, PRD 83, 083518) to evaluate the scale-dependent bias in the presence of primordial non-Gaussianity. The integrated perturbation theory is a general framework of nonlinear perturbation theory, in which a broad class of bias models can be incorporated into perturbative evaluations of biased power spectrum and higher-order polyspectra. Approximations such as the high-peak limit or the peak-background split are not necessary to derive the scale-dependent bias in this framework. Applying the halo approach, previously known formulas are re-derived as limiting cases of a general formula in this work, and it is implied that modifications should be made in general situations. Effects of redshift-space distortions are straightforwardly incorporated. It is found that the slope of the scale-dependent bias on large scales is determined only by the behavior of primordial bispectrum in the squeezed limit, and is not sensitive to bias models in general. It is the amplitude of scale-dependent bias that is sensitive to the bias models. The effects of redshift-space distortions turn out to be quite small for the monopole component of the power spectrum, while the quadrupole component is proportional to the monopole component on large scales, and thus also sensitive to the primordial non-Gaussianity.