Peak exclusion, stochasticity and convergence of perturbative bias expansions in 1+1 gravity

TL;DR

This paper investigates the effects of exclusion, stochasticity, and convergence in perturbative bias expansions for 1+1 gravity, providing insights into halo exclusion and clustering behavior beyond Gaussian initial conditions.

Contribution

It introduces analytical and numerical methods to study exclusion effects and bias expansion convergence in 1D cosmological fields, including nonlinear evolution impacts.

Findings

Deviations from Poisson noise at low frequencies in the power spectrum.

Exclusion effects are reduced at later times due to nonlinear evolution.

Large-scale convergence of bias expansion is confirmed, with notable deviations in exclusion zones.

Abstract

The Lagrangian peaks of a 1D cosmological random field representing dark matter are used as a proxy for a catalogue of biased tracers in order to investigate the small-scale exclusion in the two-halo term. The two-point correlation function of peaks of a given height is numerically estimated and analytical approximations that are valid inside the exclusion zone are derived. The resulting power spectrum of these tracers is investigated and shows clear deviations from Poisson noise at low frequencies. On large scales, the convergence of a perturbative bias expansion is discussed. Finally, we go beyond Gaussian statistics for the initial conditions and investigate the subsequent evolution of the two-point clustering of peaks through their Zel'dovich ballistic displacement, to clarify how exclusion effects mix up with scale-dependencies induced by nonlinear gravitational evolution. While the expected large-scale separation limit is recovered, significant deviations are found in the exclusion zone that tends in particular to be reduced at later times. Even though these findings apply to the clustering of one-dimensional tracers, they provide useful insights into halo exclusion and its impact on the two-halo term.