Issue |
A&A
Volume 477, Number 2, January II 2008
|
|
---|---|---|
Page(s) | 381 - 395 | |
Section | Cosmology (including clusters of galaxies) | |
DOI | https://doi.org/10.1051/0004-6361:20078099 | |
Published online | 06 November 2007 |
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
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 rc, 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 rc characterizes the behavior of
the mass variance, which decays for
as r-4, the fastest
decay of any mass distribution. The length-scale rc 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.
Key words: cosmology: observations / cosmology: large-scale structure of Universe / cosmology: miscellaneous
© ESO, 2007
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