Relativistic interpretation and cosmological signature of Milgrom's acceleration

Abstract

We propose in this letter a relativistic coordinate independent interpretation for Milgrom's acceleration $a_0=1.2\times 10^{-8}{cm/s}^2$ through a geometric constraint obtained from the product of the Kretschmann invariant scalar times the surface area of 2--spheres defined through suitable characteristic length scales for local and cosmic regimes, described by Schwarzschild and Friedman--Lema\^ıtre--Robertson--Walker (FLRW) geometries, respectively. By demanding consistency between these regimes we obtain an appealing expression for the empirical (so far unexplained) relation between the accelerations $a_0$ and $c{H}_0$. Imposing this covariant geometric criterion upon a FLRW model, yields a dynamical equation for the Hubble scalar whose solution matches, to a very high accuracy, the cosmic expansion rate of the $\Lambda$CDM concordance model fit for cosmic times close to the present epoch. We believe that this geometric interpretation of $a_0$ could provide relevant information for a deeper understanding of gravity

9 pages, IOP format, 3 figures

References in corpus (1)

• Emergent Gravity and the Dark Universe