I have been wondering whether one could obtain bimetric MOND from a GU-like theory.
In addition to ordinary matter and metric, bimetric MOND has an extra "metric" (which does not interact with ordinary matter, but which may or may not interact with "twin matter"), and an interaction term connecting the two metrics, built from the difference between their Levi-Civita connections, which modifies the Newtonian limit.
GU, meanwhile, features an extension of the usual gauge group by translations in the space of connections. I am still puzzling over the details, but a difference of connections shows up.
I also need to better understand torsion (in GU and in GR).
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