# Relativistic interpretation and cosmological signature of Milgrom's acceleration

## TL;DR

This paper offers a relativistic, geometric interpretation of Milgrom's acceleration, linking it to cosmological parameters and deriving a dynamical equation for the universe's expansion that aligns with the standard cosmological model.

## Contribution

It introduces a covariant geometric criterion connecting local acceleration scales to cosmic expansion, providing a novel interpretation of Milgrom's acceleration within general relativity.

## Key findings

- Derived an expression relating a0 and H0 consistent with observations.
- Obtained a dynamical equation for the Hubble scalar matching ΛCDM near present epoch.
- Proposed a geometric interpretation of a0 that may deepen understanding of gravity.

## Abstract

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