Being the largest virialised structures in the Universe, galaxy clusters are of particular interest for cosmological studies. According to the currently accepted ΛCDM model (also called concordant model), they are the result of a hierarchical formation process. In this process, clusters are the last objects to form and are, therefore, localised close to their formation place. Their density and properties are very sensitive to cosmological parameters governing the Universe. Besides, the formation of these large scale dark matter potential wells seems mainly independent from the complex processes of gas dynamics or from stellar formation rate and, therefore, depends practically only on gravitation.

As a result, the abundance of galaxy clusters (number of clusters per comoving volume per solid angle above a certain threshold) can be deduced from the geometry of the Universe and from the power spectrum of the initial density fluctuations. More precisely, the number density of clusters depends on the combination σ8 and Ωm, where σ8 is the normalisation factor of the power spectrum, Ωm is the mean matter density of the universe and its exponent depends on the mass range of the clusters that are considered. The degeneracy between s8 and Ωm can also be directly broken by considering the redshift evolution of the number density of clusters. In that case the evolution of cluster counts simultaneously offers a way to constrain the growth of structures and provides an independent measurement of Ωm.

The value of the amplitude of the power spectrum, σ8, measures the rate of growth of structures in the Universe and can also be constrained by itself. For a given geometrical probe an accurate determination of σ8 at two different times directly constrains the growth between the two epochs. This can in principle be used to determine whether the dark energy density evolves with redshift.

Being bright and sparse, galaxy clusters are also excellent tracers of large-scale structures. Their clustering properties can be used to derive complementary constraints of the cosmological parameters as demonstrated by several recent studies. Such an analysis requires coverage of very large, contiguous areas. It will reach its full potential only in the framework of next generation surveys (DES, LSST, EUCLID).

Therefore, large cluster surveys represent a powerful tool for deriving constraints on cosmological parameters. They can also be used for joint analysis, which helps controlling systematics from other experiments (CMB, SN, BAOs, etc.) as each of them has systematics of different origins. Using cluster surveys is even more relevant at a period in which large distant cluster samples are within reach and local cluster samples provide tight constraints at z=0, in particular with the Sloan Digital Sky Survey.

Unfortunately, unknown aspects of cluster physics might be a limitation to applications of these methods to cosmology, and in particular for dark energy studies. The main problem is the mass determination of the clusters. The abundance of clusters is exponentially dependant on mass, and therefore a small error in mass implies a large mistake in abundance. Hence, although changes in the equation of state of dark energy result in large variations at a given mass, the conversion between observable quantities and cluster mass is highly uncertain.

The potential of galaxy clusters and the current obstacles to use them as cosmological indicators are driving the steps of research projects in our team: controlled identification of clusters within optical surveys, issue of the cluster mass and modelling of cluster physics in general.