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

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.
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https://hal-cea.archives-ouvertes.fr/cea-01677647
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Submitted on : Monday, January 8, 2018 - 3:11:15 PM
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C. Uhlemann, S. Codis, J. Kim, C. Pichon, F. Bernardeau, et al.. Beyond Kaiser bias: mildly non-linear two-point statistics of densities in distant spheres. Monthly Notices of the Royal Astronomical Society, Oxford University Press (OUP): Policy P - Oxford Open Option A, 2016, 466, pp.2067-2084. ⟨10.1093/mnras/stw3221⟩. ⟨cea-01677647⟩

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