[Paper Review] Modified gravity or modified matter ?

Luc Blanchet|ArXiv.org|Feb 10, 2009

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes a dipolar dark matter model that unifies cold dark matter (CDM) in cosmology with modified gravity (MOND) at galactic scales by treating dark matter as a relativistic fluid with gravitational dipole moments. The model reproduces MOND phenomenology via a negative gravitational susceptibility and internal 'fifth force' binding dipoles, while remaining consistent with CMB observations and naturally linking dark energy to MOND's acceleration scale, offering a unified, effective description of dark matter and dark energy without fundamental new particles.

ABSTRACT

To the astrophysicist faced with the puzzle of dark matter, this one appears under two different aspects: on the one hand in cosmology, i.e. at very large scales, where it seems to be made of a bath of particles; on the other hand at the scale of galaxies, where it is described by a set of specific phenomena, looking incompatible with a description in terms of particles, and suggesting that we are seeing a modification of the law of gravity. Reconciling these two distinct aspects of dark matter in a single theoretical formalism is an important challenge which could lead to some new physics in action at astronomical scales.

Motivation & Objective

• To reconcile the particle-like behavior of dark matter in cosmology with its apparent modification of gravity in galaxies.
• To resolve the tension between cold dark matter (CDM) simulations predicting dense central halos and observations showing flat, core-like profiles in galaxies.
• To provide a relativistic, geometric framework that reproduces MOND phenomenology without violating the equivalence principle or introducing negative mass.
• To unify dark matter and dark energy by deriving a cosmological constant naturally from the MOND acceleration scale.
• To construct an effective field theory of dipolar dark matter that is consistent with both galactic dynamics and large-scale cosmology.

Proposed method

• Model dark matter as a relativistic fluid with a four-vector polarization field ξ^α, representing intrinsic gravitational dipole moments.
• Introduce an action principle combining Einstein-Hilbert gravity with a new action for the dipolar fluid, including a potential that enforces internal binding via a 'fifth force'.
• Derive equations of motion for the fluid and evolution equations for the dipole moment, showing deviation from geodesic motion due to internal forces.
• Use the dipole susceptibility χ < 0 to explain the enhanced gravitational field in MOND, analogous to dielectric anti-screening.
• Show that in cosmological perturbations, the dipolar fluid behaves as a pressureless perfect fluid, matching CDM predictions for CMB anisotropies.
• Derive the relation Λ ∼ a₀²/c⁴, linking the cosmological constant to the MOND acceleration scale a₀, explaining its small observed value.

Experimental results

Research questions

• RQ1 Can a single dark matter model explain both the success of CDM in cosmology and the flat rotation curves of galaxies without invoking particle dark matter?
• RQ2 How can MOND-like behavior emerge from a geometric, field-theoretic description of dark matter without violating the equivalence principle?
• RQ3 What is the role of a 'fifth force' in binding gravitational dipoles and stabilizing the dipolar medium?
• RQ4 Can a dipolar dark matter model reproduce the observed CMB power spectrum and large-scale structure formation?
• RQ5 Is there a natural connection between the cosmological constant and the MOND acceleration scale a₀?

Key findings

• The dipolar dark matter model reproduces MOND phenomenology at galactic scales through a negative gravitational susceptibility χ < 0, mimicking enhanced gravity via dipole anti-screening.
• The model predicts a 'fifth force' that binds the dipolar constituents, stabilizing the medium against gravitational collapse and enabling a static, dielectric-like background.
• In cosmological perturbations, the dipolar fluid behaves as a pressureless perfect fluid, matching the CDM model and reproducing observed CMB anisotropy patterns.
• The model naturally derives the cosmological constant as Λ ∼ a₀²/c⁴, with a value consistent with observations, resolving the cosmological constant problem at the effective level.
• The model unifies dark matter and dark energy by linking their energy scales through the MOND acceleration scale a₀, offering a single effective description across astrophysical scales.
• Despite its success, the model remains an effective theory without a fundamental quantum field theory derivation, and its predictions in strong-field regimes (e.g., Solar System) remain to be fully validated.