A&A 432, 771-781 (2005)

DOI: 10.1051/0004-6361:20041535

## Cosmological constraints from clustering properties of galaxy clusters

**A. Del Popolo**

^{1, 2}, N. Ercan^{1}and I. S. Yesilyurt^{1}^{1}Bo aziçi University, Physics Department, 80815 Bebek, Istanbul, Turkey

e-mail: antonino.delpopolo@boun.edu.tr

^{2}Dipartimento di Matematica, Università Statale di Bergamo, via dei Caniana, 2, 24127, Bergamo, Italy

(Received 25 June 2004 / Accepted 19 October 2004)

** Abstract **

In this paper, we discuss improvements of the Suto et al. (2000) model,
in the light of recent theoretical developments (new theoretical mass
functions, a more accurate mass-temperature relation
and an improved bias model) to predict the clustering properties of galaxy
clusters and to obtain constraints on cosmological parameters.
We re-derive the two-point correlation function of clusters of galaxies for
OCDM and CDM cosmological models, and we compare these results with
the observed spatial correlation function for clusters in RASS1 (ROSAT All-Sky Survey 1), and in XBACs (X-RAY Brighest Abell-Type) samples. The comparison shows that the best agreement
is obtained for the CDM model with
.
The values of the correlation length obtained, (
Mpc for CDM), are larger than those found in the literature and
comparable with the results found in Borgani et al.
(1999). In order to study the possible dependence of the clustering
properties of the X-ray clusters on the observational characteristics
defining the survey, we calculated the values of the correlation length *r*_{0}
in the catalogues where we vary the limiting X-ray flux
. The
result shows
an increase of *r*_{0} with
,
and correlation lengths that are larger than in previous
papers in literature (e.g. Moscardini et al. 2001 (hereafter MMM);
Suto et al. 2000).
These differences
are due essentially to the different *M*-*T*, mass function and bias model used
in this paper.
Then, we perform a maximum-likelihood analysis by comparing the theoretical
predictions to a set of observational data in the X-ray band (RASS1 Bright
Sample, BCS (Rosat Brightest Cluster Sample), XBACs, REFLEX (ROSAT-ESO Flux Limited X-Ray Sample)), similarly to MMM. In the framework of cold dark
matter models, we compute the constraints on cosmological parameters, such
as the matter density
, the contribution to density due
to the cosmological constant,
, the power-spectrum shape
parameter and normalization . If we fix and , at the values suggested by different observational datasets, we
obtain (for flat cosmological models with varying
cosmological constant
) constraints on the matter density parameter:
and
at the 95.4 and
99.73 per cent levels, respectively, which is 20-30% larger than the values
obtained MMM.
Leaving , and
, free
for the flat model, the constraints for are
, while for the open model
. These values are smaller than those of MMM by
about 20-30%. If we keep the values of
fixed, we obtain
the constraints in the
plane.
For the open model with
the
region for is 0.11-0.2 for it is 0.7 and 1.55.
For the flat model with
the
region has
and
The
values of obtained are larger than those of MMM by .
If we allow the shape parameter to vary, we find that the clustering
properties of clusters are almost independent of the matter density
parameter and of the presence of a cosmological constant, while they appear
to be strongly dependent on the shape parameter.

**Key words:**cosmology: large-scale structure of Universe

**©**

*ESO 2005*