Divergence of Perturbation Theory in Large Scale Structures
  We make progress towards an analytical understanding of the regime of
validity of perturbation theory for large scale structures and the nature of
some non-perturbative corrections. We restrict ourselves to 1D gravitational
collapse, for which exact solutions before shell crossing are known. We review
the convergence of perturbation theory for the power spectrum, recently proven
by McQuinn and White, and extend it to non-Gaussian initial conditions and the
bispectrum. In contrast, we prove that perturbation theory diverges for the
real space two-point correlation function and for the probability density
function (PDF) of the density averaged in cells and all the cumulants derived
from it. We attribute these divergences to the statistical averaging intrinsic
to cosmological observables, which, even on very large and "perturbative"
scales, gives non-vanishing weight to all extreme fluctuations. Finally, we
discuss some general properties of non-perturbative effects in real space and
Fourier space.
