The $a_0$ -- cosmology connection in MOND

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, $\mathrm{\Lambda }$ 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’.