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In this seminar I will present a model of gravity which breaks Lorentz invariance by the introduction of an everywhere time-like vector field, and was motivated by the Dirac-Born-Infeld type conformal scalar theory it yields for a conformally flat Universe. Besides its cosmological solutions, I will discuss exact black hole solutions, the post-Newtonian expansion and the dynamics of the scalar mode, both in Minkwoski and FRW backgrounds. Along the way we will also see how it compares (and departs from) General Relativity and other Lorentz violating theories like Horava-Lifshitz, whilst avoiding the pathologies associated with this kind of scalar mode.
