Galaxy clusters have demonstrated to be powerful probes of cosmology, since their mass and abundance depend on the cosmological model that describes the Universe and on the gravitational formation process of cosmological structures. The main challenge in using clusters to constrain cosmology is that their masses cannot be measured directly, but need to be inferred indirectly through their observable properties. The most common methods extract the cluster mass from their strong X-ray emission or from the measured redshifts of the galaxy members.
The gravitational lensing effect caused by clusters on the background galaxies is also an important trace of their total mass distribution.In the work presented within this thesis, we exploit the connection between the gravitational potential of galaxy clusters and the kinematical properties of their surroundings, in order to determine the total cluster mass. To this end we investigate in detail the dynamics of the non equilibrated region outside virialized clusters. Massive clusters attract galactic groups and larger structures against the expansion of the Universe. We determine the theoretical equations that allow us to model the motion of galaxies at any distance from the center of a cluster. Moreover, we analyze spectroscopic observations of galaxies far away from the central part of the cluster.
The main result of this study is the development of two new methods to measure the mass of galaxy clusters. One constrains the virial mass and the other extends the mass determination far outside the radius of virialization. Our tests performed on cosmological simulations and observational data validate the proposed methods. We also formalize a justification for the Jeans swindle, i.e. the inconsistency that characterizes the dynamical mass measurement of any cosmological structure, by explaining it within the framework of an expanding Universe.