Halo bias in the excursion set approach with correlated steps

Details Halo bias in the excursion set approach with correlated steps Halo bias in the excursion set approach with correlated steps

2011-05-11

arxiv.org/abs/1105.2261v2

MNRAS 419, 132 (2012)

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

7 pages, 3 figures; v2 -- minor clarifications, accepted in MNRAS

Scientific paper

10.1111/j.1365-2966.2011.19672.x

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.

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