Extension and estimation of correlations in cold dark matter models

¹ “Enrico Fermi Center”, via Panisperna 89 A, Compendio del Viminale, 00184 Rome, Italy e-mail: sylos@romal.infn.it
² “Istituto dei Sistemi Complessi” CNR, via dei Taurini 19, 00185 Rome, Italy
³ Sobolev Astronomical Institute, St.Petersburg State University, Staryj Peterhoff, 198504 St. Petersburg, Russia

Received: 15 June 2007
Accepted: 30 September 2007

Abstract

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 , is characterized by a typical length scale r_c, where , which is fixed by the physics of the early universe. Beyond this scale it becomes negative, going to zero with a tail proportional to . 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 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.