We propose in this letter a relativistic coordinate independent interpretation for Milgroms 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
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