Galaxy clusters are the largest collapsed structures in the universe, containing up to hundreds or thousands of individual galaxies. The redshift distribution and the evolution of clustering of massive clusters of galaxies can provide a direct measurement of the cosmic volume as a function of redshift as well as the growth rate of density perturbations. This is complementary to the measurement of the BAO scale, which is purely geometrical in nature. Comparison of theory to observations requires a calibration of the cluster masses. Clusters of galaxies can be identified optically by searching for concentrations of galaxies with the same velocities. J-PAS will provide a new window for accurate optical cluster detection and selection, based on the combination of photometric colors and good photo-z precision (equivalent to σv/c~1000 km/s) over all galaxies around each cluster, which will help to improve cluster completeness and purity. J-PAS will also provide the opportunity to self-calibrate the mass threshold of a given cluster sample in different ways, such as stacking weak lensing magnification measurements over the cluster position or using the (biased) amplitude of clustering in the same cluster sample. The photo-z accuracy for clusters will be improved in comparison to the galaxy photo-z by the square root of the number of galaxies in the cluster. This will result in a typical photo-z accuracy which is a few times smaller than that for galaxies. At the same time, one could use the velocity dispersion of the galaxies in each cluster to provide an estimate of the cluster mass. This should be accurate enough to have an estimate of the mass threshold of a given cluster sample, allowing to build a reliable mass function, the evolution of which can constrain Dark Energy parameters.

A cluster survey carried out over the J-PAS area also constrains cosmology through the spatial clustering of the galaxy clusters. As mentioned above, this can be done with even higher photo-z accuracy than in J-PAS. The clustering of galaxy clusters reflect the underlying clustering in the DM; these correlations contain a wealth of cosmological information, much like the information contained in the LRG correlation function, including the BAO position. Even if the number density for clusters is lower than that of LRGs, this is partially compensated by the higher (biased) clustering amplitude. We will use J-PAS cluster redshift distribution and cluster power spectrum as cosmological probes to study the density and nature of the DE. J-PAS can also be used in combination with weak lensing (also from J-PAS) and other surveys to provide accurate photo-z in a sample of clusters detected by the Sunyaev–Zel’dovich (SZ) or X-ray signatures of hot gas in clusters.