Gravitational wave cosmology beyond general relativity

In dark-energy models where a scalar field is nonminimally coupled to the spacetime geometry, gravitational waves are expected to be supplemented with a scalar mode. Such scalar fields may interact with the standard tensor waves, thereby affecting their observed amplitude, polarization and speed. Understanding the role of scalar waves is thus essential in order to design reliable gravitational-wave probes of dark energy and gravity beyond general relativity. In this talk, I will first discuss gravitational wave amplitude signatures from a large classe of alternative gravity theories and some possible limitations. I will then focus on the polarization and present degeneracies with GR lensed gravitational waves. Finally, I will explore how scalar Cherenkov radiation from high energy cosmic rays may allow to set constraints on the scalar phase velocity.