Probabilistic Lagrangian bias estimators and the cumulant bias expansion

TL;DR

This paper introduces probabilistic estimators for galaxy bias parameters using Lagrangian environment moments and proposes a cumulant-based bias expansion, improving understanding of galaxy-matter relations for cosmology.

Contribution

It develops new bias estimators based on environment moments and introduces a cumulant bias expansion framework, enhancing bias modeling accuracy.

Findings

Robust measurements of halo bias parameters, including tidal bias and spin dependence.

Cumulant biases of haloes are consistent with zero beyond second order.

Bias function is well approximated by a Gaussian, suggesting improved convergence.

Abstract

The spatial distribution of galaxies is a highly complex phenomenon currently impossible to predict deterministically. However, by using a statistical $\textit{bias}$ relation, it becomes possible to robustly model the average abundance of galaxies as a function of the underlying matter density field. Understanding the properties and parametric description of the bias relation is key to extract cosmological information from future galaxy surveys. Here, we contribute to this topic primarily in two ways: (1) We develop a new set of probabilistic estimators for bias parameters using the moments of the Lagrangian galaxy environment distribution. These estimators include spatial corrections at different orders to measure bias parameters independently of the damping scale. We report robust measurements of a variety of bias parameters for haloes, including the tidal bias and its dependence with spin at a fixed mass. (2) We propose an alternative formulation of the bias expansion in terms of "cumulant bias parameters" that describe the response of the logarithmic galaxy density to large-scale perturbations. We find that cumulant biases of haloes are consistent with zero at orders $n > 2$. This suggests that: (i) previously reported bias relations at order $n > 2$ are an artefact of the entangled basis of the canonical bias expansion; (ii) the convergence of the bias expansion may be improved by phrasing it in terms of cumulants; (iii) the bias function is very well approximated by a Gaussian -- an avenue which we explore in a companion paper.