Parametrized post-Newtonian expansion and FRW scalar perturbations inn-DBI gravity

Abstract

n-DBI gravity explicitly breaks Lorentz invariance by the introduction of a unit time-like vector field, thereby giving rise to an extra (scalar) degree of freedom. We look for observational consequences of this mode in two setups. Firstly, we compute the parametrized post-Newtonian (PPN) expansion of the metric to first post-Newtonian order. Surprisingly, we find that the PPN parameters are exactly the same as in General Relativity (GR), and no preferred-frame effects are produced. In particular this means that n-DBI gravity is consistent with all GR solar system experimental tests. We discuss the origin of such degeneracy between n-DBI gravity and GR, and suggest it may also hold in higher post-Newtonian order. Secondly, we study gravitational scalar perturbations of a Friedmann-Robertson-Walker space-time with a cosmological constant $\Lambda \geq 0$. In the case of de Sitter space, we show that the scalar mode grows as the universe expands and, in contrast with a canonical scalar field coupled to GR, it does not freeze on super horizon scales.