Abstract "Recent approaches to quantum gravity question the role of Lorentz invariance as a fundamental symmetry of Nature. This
has implications for most of the observables in gravitational physics,
also at low-energies. In this talk I will present a couple of these
models (Horava gravity and Einstein-aether) and describe how they
affect the predictions for binary pulsar and cosmological observations.
I will finally show which are the constraints form these
observations on Lorentz-violating theories of gravity."