Review talk at the international 4th Workshop on "New
Worlds in Astroparticle Physics" in Faro, Portugal, September 2003

astro-ph/0301137.

For a PDF version of the article, click
here.

For a Postscript version of the article, click
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Laboratoire d'astrophysique de l'OMP, CNRS, UPS

14, Av. E.Belin, 31 400 Toulouse, FRANCE

E-mail: Alain.Blanchard@ast.obs-mip.fr

**Abstract.** We are at a specific period of modern cosmology,
during which the large increase of the amount of data relevant to
cosmology, as well as their increasing accuracy,
leads to the idea that the determination of cosmological parameters
has been achieved with a rather good precision, may be of the order of 10%.
There is a large consensus around the so-called concordance model.
Indeed this model does fit an impressive set of
independent data, the most impressive been: CMB *C*_{l}
curve, most current matter density estimations,
Hubble constant estimation from HST, apparent acceleration of the Universe,
good matching of the power spectrum of matter fluctuations.
However, the necessary introduction of a non zero
cosmological constant is an extraordinary new mystery for physics,
or more exactly the come back of one of the ghost of modern physics
since its introduction by Einstein. Here,
I would like to emphasize that some results are established beyond
reasonable doubt, like the (nearly) flatness of the universe and the
existence of a dark non-baryonic component of the Universe.
But also that the evidence for a cosmological constant may not be as strong
as needed to be considered as established beyond doubt.
In this respect, I will argue that an Einstein-De Sitter universe
might still be a viable option. Some observations do not
fit the concordance picture, but they are generally considered as not to be
taken into account. I discuss several of
the claimed observational evidences supporting the concordance model,
and will focus more specifically on
the observational properties of clusters which offer powerful constraints
on various quantities of cosmological interest. They are particularly
interesting in constraining the cosmological density parameter, nicely
complementing
the CMB result and the supernova probe. While early estimations were
based on the of the *M*/*L* ratio, i.e. a local indirect measure
of the mean density which needs an extrapolation over several orders of
magnitude, new tests have been proposed during the last ten years which
are global in nature. Here, I will briefly discuss three of them: 1) the
evolution of the
abundance of clusters with redshift 2) the baryon fraction measured in local
clusters 3) apparent evolution of the baryon fraction with redshift.
I will show that these three independent tests lead to high matter density
for the Universe in the range 0.6 - 1. I therefore conclude that the
dominance of vacuum to the various density contributions to the Universe
is presently an interesting and fascinating possibility, but it is still
premature to consider it as an established scientific fact.

**Table of Contents**

- INTRODUCTION: THE CONTENTS OF THE UNIVERSE
- OBSERVIONS AND COSMOLOGICAL PARAMETERS
- What the CMB does actually tell us?
- Is the Universe accelerating ?
- Some reasons for caution

- THE MEAN DENSITY OF THE UNIVERSE FROM
CLUSTERS
- GLOBAL TESTS
- The evolution of the abundance of clusters
- The local temperature distribution function
- The local temperature distribution function
Omega
_{m} - Systematic uncertainties in the determination
of Omega
_{m} - An other global test : the baryon fraction in local clusters
- The baryon fraction in high redshift clusters

- CONCLUSION
- REFERENCES