Adrian59 said:
So, I would propose that unmodified GR can explain galaxy rotation curves or at least there should be a ‘maybe’ in the box. Correct me if I am wrong about the Tully-Fisher relationship but since it is a relationship between baryonic matter and galaxy rotation, maximum orbital velocity any theory that doesn’t have putative extra mass should agree with this relationship.
The Tully-Fischer relationship is a trivial corollary of the radial acceleration relationship which is basically another version of MOND. You need either DM or MG for it to work. It is completely inconsistent with unmodified GR without dark matter.
The reason that I elected to signify that TeVeS and MOG didn’t fit the standard model is because don’t these theories postulate extra fields which presumably if they exist will need an extension of the standard model of physics. I've noted your final point on nomenclature.
The pedantic point would be that GR, a classical theory, is still incompatible with the Standard Model, because there isn't a quantum gravity theory that is necessary for them to be theoretically consistent. This is a non-trivial big deal, but surely not what you intended to indicate.
Even GR or vanilla quantum gravity require extra gravitational fields beyond the SM (two of them in theories with a cosmological constant (GR) and/or dark energy (vanilla quantum gravity)).
I would normally think of TeVeS and MOG as equally compatible with the SM as GR because all of the fields added in each case are purely gravitational. GR with a cosmological constant has a scalar field and a tensor field. TeVeS and MOG have a scalar field, a tensor field and a vector field. Vanilla quantum gravity has a scalar dark energy field and a tensor graviton. MOND isn't relativistic and is admittedly an incomplete toy model, and so it doesn't really make sense to talk about it in that sense.
The non-gravitational part of the resulting complete theory wouldn't be changed in any of them except as necessary for a quantum gravity version (all of the popular live theories except Deur's are at their root classical theories).
This isn't really perfectly true, however. There is basically a solid consensus that GR, vanilla quantum gravity, TeVeS, MOG, MOND, Deur's approach, and any other attempt to integrate any remotely realistic theory of gravity in any form with the Standard Model in a quantum gravity form,
changes the beta functions (which change the values of these constants with respect to energy scale as they run) of all of the experimentally measured constants of the Standard Model (all 12 fermion mass constants, 3 boson mass constants, all 4 CKM matrix constants, all 4 PMNS constants and all 3 coupling constants).
This isn't a huge impact on the SM, but it would potentially impact, for example, gauge unification, which might happen in an alternative to the SM without gravity, but not one with it, or it could cause the SM coupling constants to unify (in principle, I haven't run the numbers on that and the exact form of the modified beta function is not a consensus issue even though the need to modify it in some manner when gravity is included is a consensus issue).
Indeed, given that all of the variations from GR take place in the weak field limit (with possible quantum gravity differences that would be the same for quantum versions of all realistic modified gravity theories), the way that any integration of quantum gravity or modified quantum gravity impacts the SM beta functions would probably be experimentally indistinguishable, even though there would be some slight differences.