Is There Scale-Dependent Bias in 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.

25 pages; v2 matches version published in JCAP (only minor changes relative to v1)

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• On the impact of galaxy bias uncertainties on primordial non-Gaussianity constraints
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• Designing an Inflation Galaxy Survey: how to measure $\sigma (f_{\mathrm{NL}})\sim 1$ using scale-dependent galaxy bias
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• Predictions for local PNG bias in the galaxy power spectrum and bispectrum and the consequences for $f_{\mathrm{NL}}$ constraints
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• Imprints of Oscillatory Bispectra on Galaxy Clustering
• Relativistic wide-angle galaxy bispectrum on the light-cone
• Biasing and the search for primordial non-Gaussianity beyond the local type
• Constraint of Void Bias on Primordial non-Gaussianity
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• Large Scale Limit of the Observed Galaxy Power Spectrum
• Light Fields during Inflation from BOSS and Future Galaxy Surveys
• General relativistic effects in the galaxy bias at second order
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• Single-Field Inflation and the Local Ansatz: Distinguishability and Consistency
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• The Physical Content of Long Tensor Modes in Cosmology
• From matter to galaxies: General relativistic bias for the one-loop bispectrum
• The spatial gauge-dependence of single-field inflationary bispectra
• Large gauge transformations, local coordinates and cosmological observables
• Relativistic second-order initial conditions for simulations of large-scale structure
• Relativistic and non-Gaussianity contributions to the one-loop power spectrum
• Breaking the Single Clock Symmetry: measuring single-field inflation non-Gaussian features
• Non-Gaussianity in the Squeezed Three-Point Correlation from the Relativistic Effects