Is There Scale-Dependent Bias in Single-Field Inflation?

TL;DR

This paper investigates whether single-field inflation produces scale-dependent halo bias in the presence of local primordial non-Gaussianity. Using the single-field consistency conditions and multiple derivations (mode coupling in synchronous gauge, coordinate-diffeomorphism arguments, and direct halo-density application), the authors show that the expected $k^{-2}$ bias term cancels when quantities are evaluated on fixed physical scales. They present a gauge-invariant framework for observed galaxy overdensity that incorporates general relativistic projection effects and is applicable to future surveys. The result provides a robust, unbiased way to test inflationary scenarios with galaxy clustering data, since a nonzero detection would rule out single-field inflation.

Abstract

Scale-dependent halo bias due to local primordial non-Gaussianity provides a strong test of single-field inflation. While it is universally understood that single-field inflation predicts negligible scale-dependent bias compared to current observational uncertainties, there is still disagreement on the exact level of scale-dependent bias at a level that could strongly impact inferences made from future surveys. In this paper, we clarify this confusion and derive in various ways that there is exactly zero scale-dependent bias in single-field inflation. Much of the current confusion follows from the fact that single-field inflation does predict a mode coupling of matter perturbations at the level of $f_{NL}^{loc} \approx -5/3$, which naively would lead to scale-dependent bias. However, we show explicitly that this mode coupling cancels out when perturbations are evaluated at a fixed physical scale rather than fixed coordinate scale. Furthermore, we show how the absence of scale-dependent bias can be derived easily in any gauge. This result can then be incorporated into a complete description of the observed galaxy clustering, including the previously studied general relativistic terms, which are important at the same level as scale-dependent bias of order $f_{NL}^{loc} \sim 1$. This description will allow us to draw unbiased conclusions about inflation from future galaxy clustering data.