The $a_0$ -- cosmology connection in MOND

Abstract

I limelight and review a potentially crucial aspect of MOND: The near equality of the MOND acceleration constant, $a_0$ -- as deduced from local, galactic phenomena -- and cosmological parameters. To wit, $a_0\sim c{H}_0\sim c^2{\Lambda }^{1/2}\sim c^2/{\ell }_U$, where $H_0$ is the present value of the Hubble-Lemaître constant, $\Lambda$ is the `cosmological constant', and ${\ell }_U$ is a cosmological characteristic length; e.g., the Hubble distance, or the de Sitter radius associated with $\Lambda$. In itself, this near equality has some important phenomenological consequences, such as the impossibility of black holes, and of cosmological strong lensing, in the MOND regime. More importantly perhaps, this `coincidence' may be a pointer to the `FUNDAMOND' -- the more basic theory underlying MOND phenomenology. The manners in which such a relation emerges in existing, underlying scheme of MOND are also reviewed, interlaced with examples of similar relations in other physical systems, between apparently-fundamental velocity, length, and acceleration constants. Such analogies may point the way to explanation of the MOND `coincidence'.

arXiv comment10 pages, 4 figures, Based on a talk at `BonnGravity2019 -- The functioning of galaxies: challenges for Newtonian and Milgromian dynamics', Bonn, September 2019

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• MOND fiducial specific angular momentum of disc galaxies
• Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND
• On the radial acceleration of disk galaxies
• Is the acceleration scale of the radial acceleration relation tracking the cosmic expansion rate?