### 7.3 PPN parameters

Preferred frame effects, as might be expected from Lorentz violating theories, are nicely summarized
in the parameterized post-Newtonian formalism, otherwise known as PPN (for a description,
see [277] or [276]). The simplest setting in which the PPN parameters might be different than
GR is in the static, spherically symmetric case. For static, spherically symmetric solutions in
vector-tensor models the only PPN parameters that do not vanish are the Eddington-Robertson-Schiff
(ERS) parameters and . For GR, . The ERS parameters for the general
Hellings-Nordvedt vector-tensor theory [145] are not necessarily unity [276], so one might
expect that the constrained aether model also has non-trivial ERS parameters. However, it
turns out that the constrained aether model with the Lagrange multiplier potential also has
for generic choices of the coefficients [103]. Therefore, at this point there is no method
by which the ERS parameters can be used to constrain Lorentz violating theories. The ERS
parameters for more complicated theories with higher rank Lorentz violating tensors are largely
unknown.
If we move away from spherical symmetry then more PPN parameters become important, in particular
,,and which give preferred frame effects. In [133] has been calculated to be

The observational limit on is [277]. Barring cancellations this translates to a very
strong bound of order on the coefficients in the aether action.