Non-linear extension of non-metricity scalar for MOND

Abstract

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.

arXiv comment6 pages

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• New models and Big Bang Nucleosynthesis constraints in $f(Q)$ gravity
• A designer approach to $f(Q)$ gravity and cosmological implications
• Late-time cosmology with phantom dark-energy in $f(Q)$ gravity
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• Aether scalar tensor theory: Linear stability on Minkowski space
• Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory
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• Relativistic Khronon Theory in agreement with Modified Newtonian Dynamics and Large-Scale Cosmology
• Constraining Exponential f(Q) Gravity with Cosmic Chronometers and Supernovae: A Data-Driven Analysis
• Aether scalar tensor theory: Hamiltonian Formalism
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• Broader view of bimetric MOND
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• Observational constraints using Bayesian statistics and Deep Learning in $f(Q)$ gravity
• Stealth black holes in Aether Scalar Tensor theory
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• Neutron stars in $f(\mathbb{Q})$ gravity