Non-perturbative probability distribution function for cosmological
  counts in cells
  We present a non-perturbative calculation of the 1-point probability
distribution function (PDF) for the spherically-averaged matter density field.
The PDF is represented as a path integral and is evaluated using the
saddle-point method. It factorizes into an exponent given by a spherically
symmetric saddle-point solution and a prefactor produced by fluctuations. The
exponent encodes the leading sensitivity of the PDF to the dynamics of
gravitational clustering and statistics of the initial conditions. In contrast,
the prefactor has only a weak dependence on cosmology. It splits into a
monopole contribution which is evaluated exactly, and a factor corresponding to
aspherical fluctuations. The latter is crucial for the consistency of the
calculation: neglecting it would make the PDF incompatible with translational
invariance. We compute the aspherical prefactor using a combination of analytic
and numerical techniques. We demonstrate the factorization of spurious enhanced
contributions of large bulk flows and their cancellation due the equivalence
principle. We also identify the sensitivity to the short-scale physics and
argue that it must be properly renormalized. The uncertainty associated with
the renormalization procedure gives an estimate of the theoretical error. For
zero redshift, the precision varies from sub percent for moderate density
contrasts to tens of percent at the tails of the distribution. It improves at
higher redshifts. We compare our results with N-body simulation data and find
an excellent agreement.
