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The $a_0$ -- cosmology connection in MOND
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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'.
Forward citations
Cited by 3 Pith papers
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Machian MOND: a variable $a_0$ in galaxy clusters
A Machian MOND extension in which the acceleration scale a0 depends on exterior cluster mass reproduces, in toy models, the factor of a few boost needed to explain galaxy cluster mass discrepancies.
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A Novel Test for MOND: Gravitational Lensing by Disc Galaxies
In MOND, high-inclination disc galaxies should have a larger four-image strong-lensing cross-section than a dark-matter halo fitted to the same rotation curve, a difference upcoming surveys could in principle detect.
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Seesaw relation between the cosmological constant and the Higgs mass
The paper suggests the Higgs mass is the geometric mean of the dark energy scale and the inflation scale, but the relation is fitted rather than independently derived.
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