The Radial Acceleration Relation (RAR) shows a strong correlation between two accelerations associated to galaxy rotation curves. The relation between these accelerations is given by a nonlinear function which depends on an acceleration scale a † . Some have interpreted this as an evidence for a gravity model, such as Modified Newtonian Dynamics (MOND), which posits a fundamental acceleration scale a 0 common to all the galaxies. However, it was later shown, using Bayesian inference, that this seems not to be the case: the a 0 credible intervals for individual galaxies were not found to be compatible among themselves. This type of test is a fundamental test for MOND as a theory for gravity, since it directly evaluates its basic assumption and this using the data that most favor MOND: galaxy rotation curves. Here we improve upon the previous analyses by introducing a more robust method to assess the compatibility between the credible intervals, in particular without Gaussian approximations. We directly estimate, using a Monte Carlo simulation, that the existence of a fundamental acceleration is incompatible with the data at more than 5σ. We also consider quality cuts in order to show that our results are robust against outliers. In conclusion, the new analysis further supports the claim that the acceleration scale found in the RAR is an emergent quantity.

General Relativity extensions based on Renormalization Group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post Newtonian limits of a realisation called Renormalization Group extended General Relativity (RGGR). Special attention is taken to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameterν , and this parameter is such that forν = 0 one fully recovers GR in the Solar System. Previously this parameter was constrained to be |ν | 10 −21 , without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the Parametrised Post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds onν , either considering or not the external potential effect. With the external potential effect the new bound reads |ν | 10 −16 . We discuss the possible consequences of this bound to the dark matter abundance in galaxies.

In this work, we investigate the possibility that the galaxy rotation curves can be explained in the framework of modified gravity models that introduce a Yukawa term in the gravitational potential. We include dark matter and assume that the fifth-force couples differently to dark matter and to baryons. We aim at constraining the modified gravity parameters β and λ, that is, the strength and the range of the Yukawa fifth force, respectively, using a set of 40 galaxy rotation curves data from the SPARC catalogue. We include baryonic gas, disk and bulge components, along with a NFW halo of dark matter. Each galaxy rotation curve is modeled with three free parameters, beside the two global Yukawa parameter. We find that the inclusion of the Yukawa term improves the χ 2 from 680.75 to 536.23 for 655 degrees of freedom. As global best-fit we obtain β = 0.34 ± 0.04 and λ = 5.61 ± 0.91kpc and a dark matter content on average 20% smaller than without the Yukawa term. The Bayesian evidence in favor of a NFW profile plus Yukawa term is higher than 8σ with respect to the standard gravity parametrization.