  The direct detection of gravitational waves by ground-based interferometers
opened an unprecedented channel to probe alternative theories of gravitation.
Several theories predict a dispersion of the gravitational waves during their
propagation, distorting the signals observed by LIGO and Virgo compared to
their predictions from general relativity. Such dispersion could induce a
modification of the luminosity distance inferred with gravitational radiation
with regards to electromagnetic radiation. By analysing two multimessenger
events, we set constraints on a large class of proposed theories, including
extra-dimensional and scalar-tensor theories. The multimessenger events are the
binary neutron star merger GW170817 associated to GRB170817A, and the binary
black hole merger GW190521 with postulated candidate electromagnetic
counterpart ZTF19abanrhr. Without relying on multimessenger emission, a class
of proposed theories predict a frequency-dependent dispersion of the
gravitational waves breaking Lorentz invariance. By analysing 31 GW events from
binary-black holes coalescence, we constrain several coefficients
parameterising Lorentz violation, including the best constraint on the graviton
mass.

General Relativity and Quantum Cosmology