Halo bias in the excursion set approach with correlated steps

TL;DR

This paper investigates how real-space correlations in the initial density field affect halo bias predictions in the excursion set approach, providing corrections to improve the accuracy of cosmological parameter constraints.

Contribution

It extends the excursion set approach to include real-space correlations, highlighting the importance of accounting for these effects in halo bias predictions.

Findings

Ignoring real-space correlations leads to biased halo bias estimates.

Correcting for real-space correlations improves agreement with simulations.

Misinterpretation of bias measurements can bias cosmological constraints.

Abstract

In the Excursion Set approach, halo abundances and clustering are closely related. This relation is exploited in many modern methods which seek to constrain cosmological parameters on the basis of the observed spatial distribution of clusters. However, to obtain analytic expressions for these quantities, most Excursion Set based predictions ignore the fact that, although different k-modes in the initial Gaussian field are uncorrelated, this is not true in real space: the values of the density field at a given spatial position, when smoothed on different real-space scales, are correlated in a nontrivial way. We show that when the excursion set approach is extended to include such correlations, then one must be careful to account for the fact that the associated prediction for halo bias is explicitly a real-space quantity. Therefore, care must be taken when comparing the predictions of this approach with measurements in simulations, which are typically made in Fourier-space. We show how to correct for this effect, and demonstrate that ignorance of this effect in recent analyses of halo bias has led to incorrect conclusions and biased constraints.