  We present new perturbation theory (PT) predictions in the Spherical Collapse
(SC) model for the 2-point moments of the large-scale distribution of dark
matter density in the universe. We assume that these fluctuations grow under
gravity from small Gaussian initial conditions. These predictions are compared
with numerical simulations and with previous PT results to assess their domain
of validity. We find that the SC model provides in practice a more accurate
description of 2-point moments than previous tree-level PT calculations. The
agreement with simulations is excellent for a wide range of scales (5-50 Mpc/h)
and fluctuations amplitudes (0.02-2 variance). When normalized to unit variance
these results are independent of the cosmological parameters and of the initial
amplitude of fluctuations. The 2-point moments provide a convenient tool to
study the statistical properties of gravitational clustering for fairly
non-linear scales and complicated survey geometries, such as those probing the
clustering of the Ly-alpha forest. In this context, the perturbative SC
predictions presented here, provide a simple and novel way to test the
gravitational instability paradigm.
