EDMs, i.e. electric dipole moments of electrons, neutrons or nuclei are sensitive probes for new physics beyond the Standard Model of particle physics. In the present project, we propose to measure the EDM of those systems embedded in a cryogenic solid matrix of inert gas or hydrogen. Matrices offer unprecedented sample sizes while maintaining characteristics of an atomic physics experiment, such as the possibility of manipulation by lasers. An EDM experiment on molecules in inert gas matrices has the potential to reach a statistical sensitivity of the order of 1e–36 e cm; a value beyond that of any other proposed technique. With this project, in a strong collaboration between experimental (LAC, ISMO,LPL) and theoretical (CIMAP) groups, we first aim at performing a detailed investigation of all limiting effects (mainly the ones limiting the optical pumping performance and coherence time) using Cs atoms. This should provide a first proof of principle EDM measurement and set the ground for precise study of systematic effects which will allow EDMMA to reach unprecedented precision