What is modified gravity and how to differentiate it from particle dark matter?

Abstract

An obvious criterion to classify theories of modified gravity is to identify their gravitational degrees of freedom and their coupling to the metric and the matter sector. Using this simple idea, we show that any theory which depends on the curvature invariants is equivalent to general relativity in the presence of new fields that are gravitationally coupled to the energy-momentum tensor. We show that they can be shifted into a new energy-momentum tensor. There is no a priori reason to identify these new fields as gravitational degrees of freedom or matter fields. This leads to an equivalence between dark matter particles gravitationally coupled to the standard model fields and modified gravity theories designed to account for the dark matter phenomenon. Due to this ambiguity, it is impossible to differentiate experimentally between these theories and any attempt of doing so should be classified as a mere interpretation of the same phenomenon.

arXiv comment12 pages

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• Model Independent analysis of MeV scale dark matter: I. Cosmological constraints
• Covariant singularities in Quantum Field Theory and Quantum Gravity
• Acausality in Superfluid Dark Matter and MOND-like Theories
• Model Independent analysis of MeV scale dark matter: II. Implications from $e^{-}{e}^{+}$ colliders and Direct Detection
• The non-minimal coupling constant and the primordial de Sitter state
• Fab Four Effective Field Theory Treatment
• Magnetogenesis in Cyclical Universe
• Singularity theorems in the effective field theory for quantum gravity at second order in curvature
• Gravity and Nonlinear Symmetry Realisation
• Quartet-metric/multi-component gravity: scalar graviton as emergent dark substance
• Hypersymmetry of gravitational and inertial masses in relativistic field theories
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