  In models of modified gravity, extra degrees of freedom usually appear. They
must be removed from the spectrum because they may indicate the presence of
instabilities and because otherwise the model might not agree with observation.
In the present letter, we will discuss a model that modifies General Relativity
through the addition of a Lorentz-violating potential-like term for the metric.
No additional propagating modes and no classical instabilities are present. The
model departs from GR only in the extreme infrared region, and the cosmological
evolution contains a bounce when the size of the Universe is of the same order
of the added deformation.
