Non-linear extension of non-metricity scalar for MOND
  General Relativity enjoys the freedom of different geometrical
interpretations in terms of curvature, torsion or non-metricity. Within this
geometrical trinity, a simpler geometrical formulation of General Relativity
manifests itself in the latter, where gravity is entirely attributed to
non-metricity. In this Letter, we consider non-linear extensions of Coincident
General Relativity $f(\mathring{\mathbb{Q}})$ for phenomenological applications
on both cosmological as well as galactic scales. The theory not only delivers
dark energy on large scales but also recovers MOND on galactic scales, together
with implications for the early universe cosmology. To the best of our
knowledge, this represents the first relativistic, covariant, and ghost-free
hybrid-formulation of MOND which recovers both, General Relativity and MOND in
the appropriate limits and reconciles expected cosmological behavior. We
further illustrate that previous bimetric formulations of MOND generically
suffer from ghost instabilities and $f(\mathring{\mathbb{Q}})$ crystalizes as a
unique ghost-free theory.
