Two-point moments in cosmological large-scale structure – I. Theory and comparison with simulations

We present new perturbation theory (PT) predictions in the spherical collapse (SC) model for the two-point moments of the large-scale distribution of dark matter density in the Universe. We assume that these fluctuationsgrow 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 two-point moments than previous tree-level PT calculations. The agreement with simulations is excellent for a wide range of scales (5-50h - 1 Mpc) and fluctuation amplitudes (σ 2 ≃ 0.02-2). When normalized to unit variance these results are independent of the cosmological parameters and of the initial amplitude of fluctuations. The two-point moments provide a convenient tool for studying the statistical properties of gravitational clustering for fairly non-linear scales and complicated survey geometries, such as those probing the clustering of the Lya forest. In this context, the perturbative SC predictions presented here provide a simple and novel way of testing the gravitational instability paradigm.