A rather nice summary of the current state of alternative theories of gravity. TLDR : they don't work. Which is likely to make a lot of people very annoyed and be widely regarded as a bad move, but there we go.
There doesn't seem much point in extracting quotes from a fairly comprehensive summary article (nevertheless I have done so anyway]. The only thing I would add to this is that modifying gravity doesn't have the nice simple effects of only changing galactic rotation curves as the article implies : it causes a bunch of other, weirder effects, of which by far and away the best explanation can be found here : http://burro.astr.cwru.edu/ArnoldMOND/ahnoldmond.html
Then there is TeVeS (tensor-vector-scalar), MOND’s relativistic cousin. While MOND is a modification of Newtonian gravity, TeVeS is an attempt to take the general idea of MOND and make it into a full mathematical theory that can be applied to the universe as a whole — not just to relatively small objects like solar systems and galaxies. It also explains the rotation curves of galaxies by making gravity stronger on their outskirts. But TeVeS does so by augmenting gravity with “scalar” and “vector” fields that “essentially amplify gravity,” said Fabian Schmidt, a cosmologist at the Max Planck Institute for Astrophysics in Garching, Germany.
Consider the neutron-star merger. At the same time that the Laser Interferometer Gravitational-Wave Observatory (LIGO) spotted the gravitational waves emanating from the event, the space-based Fermi satellite spotted a gamma ray burst from the same location. The two signals had traveled across the universe for 130 million years before arriving at Earth just 1.7 seconds apart.
These nearly simultaneous observations “brutally and pitilessly murdered” TeVeS theories, said Paulo Freire, an astrophysicist at the Max Planck Institute for Radio Astronomy in Bonn, Germany. “Gravity and gravitational waves propagate at the speed of light, with extremely high precision — which is not at all what was predicted by those [alternative] theories.”
There are also so-called Galileon theories — part of a class of theories called Horndeski and beyond-Horndeski — which attempt to get rid of dark energy. These modifications of general relativity also introduce a scalar field. There are many of these theories (Brans-Dicke theory, dilaton theories, chameleon theories and quintessence are just some of them), and their predictions vary wildly among models. But they all change the expansion of the universe and tweak the force of gravity.
These also predict that gravitational waves propagate more slowly than light. The neutron-star merger killed those off too, Schmidt said.
https://www.quantamagazine.org/troubled-times-for-alternatives-to-einsteins-theory-of-gravity-20180430/
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