Scale Invariance at low accelerations (aka MOND) and the dynamical   anomalies in the Universe
  Galactic systems, and the Universe at large, exhibit large dynamical anomalies: The observed matter in them falls very short of providing enough gravity to account for their dynamics. The mainstream response to this conundrum is to invoke large quantities of `dark matter' -- which purportedly supplies the needed extra gravity -- and also of `dark energy', to account for further anomalies in cosmology, such as the observed, accelerated expansion. The MOND paradigm offers a different solution: a breakdown of standard dynamics (gravity and/or inertia) in the limit of low accelerations -- below some acceleration $a_0$. In this limit, dynamics become space-time scale invariant, and is controlled by a gravitational constant $\mathcal{A}_0\equiv Ga_0$, which replaces Newton's $G$. With the new dynamics, the various detailed manifestations of the anomalies in galaxies are predicted with no need for dark matter. The cosmological anomalies could, but need not have to do with small accelerations. For example, the need for dark matter in accounting for the expansion history of the Universe is eliminated if the relevant gravitational constant is $\approx 2\pi G$. Such a `renormalization' of $G$ could be a dimensionless parameter of a MOND theory. The constant $a_0$ turns out to carry cosmological connotations, in that $2\pi a_0\approx cH_0\approx c^2(\Lambda/3)^{1/2}$, where $H_0$ is the present expansion rate of the Universe, and $\Lambda$ the measured `cosmological constant'. There are MOND theories in which this `coincidence' is natural. I draw on enlightening historical and conceptual analogies from quantum theory to limelight aspects of MOND. I also explain how MOND may have strong connections with effects of the quantum vacuum on local dynamics. 
Mordehai Milgrom
astro-ph.GA astro-ph.CO gr-qc hep-ph