Stochastic Bias from Non-Gaussian Initial Conditions

TL;DR

This paper demonstrates that multi-source inflationary models with non-Gaussian initial conditions can produce a stochastic, scale-dependent halo bias, with a general formula derived for both stochastic and non-stochastic components.

Contribution

It introduces a general formula for stochastic halo bias in multi-source inflation models with non-Gaussian initial conditions, linking it to N-point cumulants of curvature perturbations.

Findings

Stochastic bias arises if the four-point function's collapsed limit exceeds the squared three-point function.

Derived formulas for stochastic and non-stochastic bias components using two different methods.

Applicable to models like curvaton and quasi-single field inflation.

Abstract

In this article, we show that a stochastic form of scale-dependent halo bias arises in multi-source inflationary models, where multiple fields determine the initial curvature perturbation. We derive this effect for general non-Gaussian initial conditions and study various examples, such as curvaton models and quasi-single field inflation. We present a general formula for both the stochastic and the non-stochastic parts of the halo bias, in terms of the N-point cumulants of the curvature perturbation at the end of inflation. At lowest order, the stochasticity arises if the collapsed limit of the four-point function is boosted relative to the square of the three-point function in the squeezed limit. We derive all our results in two ways, using the barrier crossing formalism and the peak-background split method. In a companion paper, we prove that these two approaches are mathematically equivalent.