  We propose in this letter a relativistic coordinate independent
interpretation for Milgrom's acceleration $a_{0}=1.2 \times 10^{-8}
\hbox{cm/s}^{2}$ 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\^\i 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 $a_0$ 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
