On the origin of transient features in cosmological N-Body Simulations

We study the effect of gravitational clustering at small scales on larger scales by studying mode coupling between virialised halos. We build on the calculation by Peebles (1974) where it was shown that a virialised halo does not contribute any mode coupling terms at small wave numbers $k$. Using a perturbative expansion in wave number, we show that this effect is small and arises from the deviation of halo shapes from spherical and also on tidal interactions between halos. We connect this with the impact of finite mass resolution of cosmological N-Body simulations on the evolution of perturbations at early times. This difference between the expected evolution and the evolution obtained in cosmological N-Body simulations can be quantified using such an estimate. We also explore the impact of a finite shortest scale up to which the desired power spectrum is realised in simulations. Several simulation studies have shown that this effect is small in comparison with the effect of perturbations at large scales on smaller scales. It is nevertheless important to study these effects and develop a general approach for estimating their magnitude. This is especially relevant in the present era of precision cosmology. We provide basic estimates of the magnitude of these effects and their power spectrum dependence. We find that the impact of small scale cutoff in the initial power spectrum and discreteness increases with $(n+3)$, with $n$ being the index of the power spectrum. In general, we recommend that cosmological simulation data should be used only if the scale of non-linearity, defined as the scale where the linearly extrapolated {\it rms} amplitude of fluctuations is unity, is larger than the average inter-particle separation.