2008A&A...477..381S

We discuss the large-scale properties of standard cold dark-matter cosmological models characterizing the main features of the power spectrum, of the two-point correlation function, and of the mass variance. Both the real-space statistics show a very well-defined behavior on large enough scales, for their amplitudes to become smaller than unity. The correlation function, in the range 0<ξ(r)<1, is characterized by a typical length scale r_c, where ξ(r_c)=0, which is fixed by the physics of the early universe. Beyond this scale it becomes negative, going to zero with a tail proportional to -(r^–4). These anti-correlations thus represent an important observational challenge for verifying models in real space. The same length scale r_c characterizes the behavior of the mass variance, which decays for r>r_c as r^–4, the fastest decay of any mass distribution. The length-scale r_c defines the maximum extension of (positively correlated) structures in these models. These are the features expected for the dark-matter field: however galaxies, which represent a biased field, may differ in their behaviors, which we analyze. We then discuss the detectability of these real-space features by considering several estimators of the two-point correlation function. By making tests on numerical simulations, we emphasize the important role of finite size effects, which should always be controlled for careful measurements.