Two is better than one: joint statistics of density and velocity in
  concentric spheres as a cosmological probe
  The analytical formalism to obtain the probability distribution functions
(PDFs) of spherically-averaged cosmic densities and velocity divergences in the
mildly non-linear regime is presented. A large-deviation principle is applied
to those cosmic fields assuming their most likely dynamics in spheres is set by
the spherical collapse model. We validate our analytical results using
state-of-the-art dark matter simulations with a phase-space resolved velocity
field finding a 2% percent level agreement for a wide range of velocity
divergences and densities in the mildly nonlinear regime (~10Mpc/h at redshift
zero), usually inaccessible to perturbation theory. From the joint PDF of
densities and velocity divergences measured in two concentric spheres, we
extract with the same accuracy velocity profiles and conditional velocity PDF
subject to a given over/under-density which are of interest to understand the
non-linear evolution of velocity flows. Both PDFs are used to build a simple
but accurate maximum likelihood estimators for the redshift evolution of the
variance of both the density and velocity divergence fields, which have smaller
relative errors than their sample variances when non-linearities appear. Given
the dependence of the velocity divergence on the growth rate, there is a
significant gain in using the full knowledge of both PDFs to derive constraints
on the equation of state of dark energy. Thanks to the insensitivity of the
velocity divergence to bias, its PDF can be used to obtain unbiased constraints
on the growth of structures ($\sigma_8$,f) or it can be combined with the
galaxy density PDF to extract bias parameters.
