Well-motivated theories with nonzero PPN ζ?

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Does anyone know of any well-motivated theories of gravity -- preferably viable ones -- that have nonzero values of the PPN ζ parameters, which describe momentum nonconservation?

In http://relativity.livingreviews.org/Articles/lrr-2006-3/articlesu6.html#x12-200003.3 [Broken] , table 3 shows some theories that are probably well motivated, but none of them have any of the ζi nonzero.

Presumably any such theory would be strongly constrained by lunar laser ranging.
 
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Does anyone know of any well-motivated theories of gravity -- preferably viable ones -- that have nonzero values of the PPN ζ parameters, which describe momentum nonconservation?

In http://relativity.livingreviews.org/Articles/lrr-2006-3/articlesu6.html#x12-200003.3 [Broken] , table 3 shows some theories that are probably well motivated, but none of them have any of the ζi nonzero.

Presumably any such theory would be strongly constrained by lunar laser ranging.
I don't know any offhand (maybe the Belinfante-Swihart theory (non-viable)), but perhaps you can find something
useful on this site

http://www.phy.olemiss.edu/~luca/
 
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