The search for new physical degrees of freedom and the dark sector of cosmology

The dark sector can be interpreted as the need for new degrees of freedom, either geometrical or physical. This has led to the development of many methods to test the underlying hypothesis of the standard cosmological model. After briefly reviewing the complementarity of these existing tests, I will focus on the tests of General Relativity on astrophysical scales and in particular of fundamental constants to probe the validity of the equivalence principle. This will highlight the complementarity of local and global experiments to constrain theory beyond the standard model.