Relativistic interpretation and cosmological signature of Milgrom's acceleration
Abstract
We propose in this letter a relativistic coordinate independent interpretation for Milgrom's acceleration a0=1.2 × 10-8 cm/s2 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\ tre--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 a0 and c H0. 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 concordance model fit for cosmic times close to the present epoch. We believe that this geometric interpretation of a0 could provide relevant information for a deeper understanding of gravity