PPN expansion and FRW scalar perturbations in n-DBI gravity
  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.
