Cosmology with GTC. A combined mm-optical galaxy cluster survey

The CMB Planck satellite (ESA) will provide a catalogue of nearly 30000 galaxy clusters (Sunyaev-Zel'dovich effect) between redshift 0 and approx. 2-3 (depending on the cosmological model). This hughe catalogue of clusters will allow detailed studies of the evolution of the cluster population with redshift which will constrain the cosmological model. The identification of the high redshift clusters should be done with a large telescope (like GTC) since Planck data alone will not provide any clue about the redshift of the clusters. In this work we show that an optical follow up of only 300 clusters (randomly selected from the Planck catalogue) is needed in order to distinguish models with or without a cosmological constant.