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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 [277Jump To The Next Citation Point] or [276Jump To The Next Citation Point]). 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 g and b. For GR, b = g = 1. 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 b = g = 1 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 a1,a2,and a3 which give preferred frame effects. In [133] a2 has been calculated to be

3 2 2 a2 = - 2c1 +-4c3(c2-+-c3) +-c1(3c2-+-5c3 +-3c4) +-c1[(6c3--c4)(c3 +-c4)-+-c2(6c3 +-c4)]. (113) 2c1(c1 + c2 + c3)
The observational limit on a2 is -7 |a2| < 4 × 10 [277]. Barring cancellations this translates to a very strong bound of order -7 10 on the coefficients ci in the aether action.


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