Halo bias in the excursion set approach with correlated steps

Authors

  • Aseem Paranjape,

    Corresponding author
    1. The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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  • Ravi K. Sheth

    1. The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
    2. Center for Particle Cosmology, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA
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E-mail: aparanja@ictp.it

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 non-trivial 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 while 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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