Beyond Kaiser bias: mildly non-linear two-point statistics of densities in distant spheres

C. Uhlemann; S. Codis; J. Kim; C. Pichon; F. Bernardeau; D. Pogosyan; C. Park; B. L 'Huillier

Beyond Kaiser bias: mildly non-linear two-point statistics of densities in distant spheres

C. Uhlemann ¹ S. Codis ² J. Kim ³ C. Pichon ^{4, 3} F. Bernardeau ^{4, 5} D. Pogosyan ^{4, 6} C. Park ³ B. L 'Huillier ^{3, 7}

1 UTRECHT U. - Institute for Theoretical Physics

2 CITA - Canadian Institute for Theoretical Astrophysics

3 KIAS - Korea Institute for Advanced Study

4 IAP - Institut d'Astrophysique de Paris

5 IPHT - Institut de Physique Théorique - UMR CNRS 3681

6 Department of Physics, University of Alberta, Edmonton, Alberta, Canada

7 KASI - Korea Astronomy and Space Science Institute

Abstract : Simple parameter-free analytic bias functions for the two-point correlation of densities in spheres at large separation are presented. These bias functions generalize the so-called Kaiser bias to the mildly non-linear regime for arbitrary density contrasts as b(ρ) − b(1) ∝ (1 − ρ$^{−13/21}$)ρ$^{1+n/3}$ with b(1) = −4/21 − n/3 for a power-law initial spectrum with index $n$. The derivation is carried out in the context of large deviation statistics while relying on the spherical collapse model. A logarithmic transformation provides a saddle approximation which is valid for the whole range of densities and shown to be accurate against the 30 Gpc cube state-of-the-art Horizon Run 4 simulation. Special configurations of two concentric spheres that allow to identify peaks are employed to obtain the conditional bias and a proxy to BBKS extrema correlation functions. These analytic bias functions should be used jointly with extended perturbation theory to predict two-point clustering statistics as they capture the non-linear regime of structure formation at the percent level down to scales of about 10 Mpc/h at redshift 0. Conversely, the joint statistics also provide us with optimal dark matter two-point correlation estimates which can be applied either universally to all spheres or to a restricted set of biased (over-or underdense) pairs. Based on a simple fiducial survey, this estimator is shown to perform five times better than usual two-point function estimators. Extracting more information from correlations of different types of objects should prove essential in the context of upcoming surveys like Euclid, DESI, PFS or LSST.

Keywords : cosmology: theory large-scale structure of Universe methods: analytical numerical

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Journal articles

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Physics [physics]

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