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-Lema\^{i}tre 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'.