Halo bias in the peak model. A first-principles non-parametric approach

TL;DR

This paper introduces a first-principles, non-parametric method to accurately predict halo bias in structure formation, addressing limitations of previous models and aligning well with simulation results.

Contribution

It applies the CUSP formalism to derive bias parameters from first principles without free parameters, improving the theoretical understanding of halo bias.

Findings

Predicted Eulerian linear halo bias matches simulation results.

Small deviations at low masses are due to halo-finding algorithm artifacts.

Addresses limitations of PS, ES, and ESP models in reproducing halo bias.

Abstract

The Press-Schechter (PS) and excursion set (ES) models of structure formation fail in reproducing the halo bias found in simulations, while the excursion set-peaks (ESP) formalism built in the peak model reproduces it only at high masses and does not address in a fully satisfactory manner peak nesting and the mass and time of ellipsoidal collapse of triaxial peaks in the Gaussian-smoothed density field. Here we apply the CUSP formalism fixing all these issues from first principles and with no free parameters to infer the Lagrangian local peak bias parameters, which adopt very simple analytic expressions similar to those found in the PS and ES models. The predicted Eulerian linear halo bias recovers the results of simulations. More specifically, we show that the only small departure observed at intermediate and low masses can be due to the spurious halo splitting and grouping caused by the Spherical Overdensity halo-finding algorithm used in simulations.