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