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ohwilleke

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My question is whether this is as viable a relativistic generalization of a MOND-like gravity modification as it seems to be, and if it has flaws, what are they.

A recent paper asserts that it does so quite well:

In 2016 McGaugh, Lelli and Schombert established a universal Radial Acceleration Relation for centripetal accelerations in spiral galaxies.Their work showed a strong correlation between observed centripetal accelerations and those predicted by luminous Newtonian matter alone. Through the use of the fitting function that they introduced,mass discrepancies in spiral galaxies can be constrained in a uniform manner that is completely determined by the baryons in the galaxies.Here we present a new empirical plotof the observed centripetal accelerations and the luminous Newtonian expectations,which more than doubles the number of observed data points considered by McGaugh et al. while retaining the Radial Acceleration Relation.If this relation is not to be due to dark matter, it would then have to be due to an alternate gravitational theory that departs from Newtonian gravity in some way. In this paper we show how the candidate alternate conformal gravity theory can provide a natural description of the Radial Acceleration Relation, without any need for dark matter or its free halo parameters.We discuss how the empirical Tully-Fisher relation follows as a consequence of conformal gravity.

James G. O'Brien, et al., "Radial Acceleration and Tully-Fisher Relations in Conformal Gravity" (December 7, 2018) (Submitted to JPCS for the proceedings of the International Association of Relativistic Dynamics 2018 meeting in Merida).

I transcribed and formatted a quotation from that paper setting forth the key equations in a post at my blog (which I am not relying upon as an independent source, just a place where I cut and pasted some the article above) if you'd like to review them, but it took about 40 minutes to do that and I have time to reproduce that tedious formatting in this post (and don't know a way to port the formatting I did from blogger format), I'd welcome the efforts of anyone who did.

An earlier development of the Conformal Gravity theory is found at:

We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity.As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory.We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source. Moreover, because it is this very coupling that fixes the strength of the gravitational field commutators, the gravity sector zero-point energy density and pressure fluctuations are then able to identically cancel the zero-point fluctuations associated with the matter sector. In addition, we show that when the conformal symmetry is spontaneously broken, the zero-point structure automatically readjusts so as to identically cancel the cosmological constant term that dynamical mass generation induces. We show that the macroscopic classical theory that results from the quantum conformal theoryincorporates global physics effects thatprovide for a detailed accounting of a comprehensive set of 138 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever.With these global effects eliminating the need for dark matter, we see that invoking dark matter in galaxies could potentially be nothing more than an attempt to describe global physics effects in purely local galactic terms. Finally, we review some recent work by 't Hooft in which a connection between conformal gravity and Einstein gravity has been found.

Philip D. Mannheim, "Making the Case for Conformal Gravity" (October 27, 2011) (Presentation at the International Conference on Two Cosmological Models, Universidad Iberoamericana, Mexico City, November 17-19, 2010. Updated final version, contains many new footnotes. To appear in Foundations of Physics).