| Abstract: | Lorentz invariance is one of the best tested symmetries of particle physics. When extended to gravitational physics, one general relativity emerges as the most natural theory of gravitation. But general relativity is not a renormalizable theory, and its quantization requires to modify or complete it at high energies. In this talk I will first describe how this can be achieved if one considers that Lorentz invariance is broken by the presence of a preferred time direction (Horava gravity). The bulk of the talk will be devoted to explain how to parametrize the deviations from general relativity and where to look for observable effects. The models with a preferred time direction include extra massless gravitational degrees of freedom, which affects the dynamics of gravitation at all scales. I will make special emphasis on the implications for cosmology and the relation with violations of the equivalence principle. |