• Clusters are the largest bound or nearly objects in the Universe, luminous enough to be seen at large distances.

• The hot intercluster gas emits strongly in X-rays and thus clusters can be unambiguously located up to very large distances.

In an Ω<1 universe clusters of galaxies formed early and have stopped evolving while in Ω=1 the formed much latter and are still in the process of formation.

Therefore in Ω<1 universes, clusters of galaxies should be more relaxed with regular density profiles.

This can be understood from the growth of the density perturbations, δ, in different Ω universes:

in Ω=1

in Ω=0

and from the evolution of the density parameter Ω(z).

which shows that even if , if then and therefore density perturbations will grow as in an universe until and the will freeze thereafter. The redshift of transition between the EdeS phase of an Ω<1 universe can be found by inspecting Einsteins field equations for a homogeneous and isotropic fluid:

Evaluating at present time we have

ie.,the curvature term starts dominating the density term if

• Cluster abundances vs z (Press & Schechter formalism) ΰ Ω<1
• Evolution of relation:  ΰ Ω=1

1. Existence of significant substructure (>20% of mass, bimodality - optical + X-ray observations)
2. Regularity of X-ray emission profiles
3. Better study above as a function of redshift to overcome problems of subjectivity of "substructure" definition.

We have initiated such a project to study the 500 optical APM clusters and archived ROSAT X-ray data + new XMM observations (Basilakos, Plionis, Maddox & Georgantopoulos in preparation).

Locally no evidence for cluster galaxy alignments with cluster potential (except for central BCG which is probably due to anisotropic mergers along large-scale filamentary structure - West 1993)

However Plionis, Maurocordato & Proust (1998) have found, using CFHT CCD observations, that Abell 521 at z=0.25 show significant alignments of cluster galaxies with cluster potential and also an ongoing merger event. These alignments cannot be produced by tidal effects, between protoclusters, since the nearest rich cluster is at distance of 80 Mpc.

• Scarce analytical work on evolution of alignments.
• N-body simulations still don't cover the dynamical range needed to simulated galaxies and the whole cluster simultanesoulsy.

If such alignments are common place at z» 0.2 then this would imply recent cluster evolution and Ω=1 would be preferred.