[Paper Review] Phenomenology of the Modified Newtonian Dynamics and the Concordance Cosmological Scenario

Luc Blanchet, Alexandre Le Tiec|ArXiv.org|Jul 8, 2008

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes a relativistic model within standard general relativity where dark matter emerges not as particles but as a polarizable dipolar medium, explaining MOND phenomenology via gravitational polarization. The model naturally reproduces the $Λ$-CDM scenario at early times and derives the cosmological constant $Λ \sim a_0^2$, reconciling MOND-like galactic dynamics with large-scale cosmology without modifying gravity or introducing new fundamental fields beyond standard relativity.

ABSTRACT

After reviewing the modified Newtonian dynamics (MOND) proposal, we advocate that the associated phenomenology may actually not result from a modification of Newtonian gravity, but from a mechanism of "gravitational polarization" of some dipolar medium playing the role of dark matter. We then build a relativistic model within standard general relativity to describe (at some phenomenological level) the dipolar dark matter polarizable in a gravitational field. The model naturally involves a cosmological constant, and is shown to reduce to the concordance cosmological scenario (Lambda-CDM) at early cosmological times. From the mechanism of gravitational polarization, we recover the phenomenology of MOND in a typical galaxy at low redshift. Furthermore, we show that the cosmological constant Lambda scales like a0^2, where a0 is the constant MOND acceleration scale, in good agreement with observations.

Motivation & Objective

• To reconcile the success of the $Λ$-CDM model at cosmological scales with the empirical success of MOND at galactic scales.
• To provide a physical mechanism for MOND-like dynamics without modifying Newtonian gravity, instead attributing it to gravitational polarization of a dipolar medium.
• To derive the cosmological constant $Λ$ from the MOND acceleration scale $a_0$, achieving consistency with observations.
• To construct a relativistic model within standard general relativity that reduces to $Λ$-CDM at early times and reproduces MOND at low redshift.

Proposed method

• Formulate a relativistic action for a dipolar fluid with a scalar potential $\phi$ and polarization field $\bm{\Pi}_{\perp}$, coupled to gravity via a non-minimal coupling.
• Derive the modified Poisson equation (23) from the field equations, showing that the dipolar dark matter density $\rho = \sigma - \bm{\nabla}\cdot\bm{\Pi}_{\perp}$ includes both monopolar and dipolar contributions.
• Apply the weak clustering hypothesis, assuming $\sigma \ll \rho_{\text{b}}$ and $\bm{v} \approx \mathbf{0}$, to ensure the dipole field $\bm{\Pi}_{\perp}$ aligns with the gravitational field $\bm{g}$.
• Use the equilibrium condition $\bm{g} \simeq \hat{\bm{\Pi}}_{\perp} \mathcal{W}'$ to derive the MOND-like susceptibility $\chi(g) = -1 + \frac{g}{a_0} + \mathcal{O}(g^2)$, matching the MOND interpolation function.
• Show that the model reduces to the standard $\Lambda$-CDM scenario at early cosmological times by matching the effective stress-energy tensor to a cosmological constant.
• Derive the relation $\Lambda \sim a_0^2$ from the model’s parameters, consistent with observational constraints.

Experimental results

Research questions

• RQ1 Can the phenomenology of MOND be explained not by modifying gravity, but by a mechanism of gravitational polarization in a dipolar medium?
• RQ2 Does a relativistic model based on standard general relativity with a polarizable dipolar fluid reproduce both the $\Lambda$-CDM cosmology at early times and MOND behavior at low redshift?
• RQ3 Can the cosmological constant $\Lambda$ emerge naturally from the MOND acceleration scale $a_0$ in such a model?
• RQ4 Is the weak clustering hypothesis sufficient to ensure that the dipolar fluid contributes negligibly to the total mass density, allowing MOND to fit galactic rotation curves?
• RQ5 How does the polarization of the dipolar medium lead to a modified gravitational response that mimics MOND without altering the underlying gravitational action?

Key findings

• The model reproduces the MOND phenomenology in a typical galaxy at low redshift through gravitational polarization of a dipolar medium, without modifying Newtonian gravity.
• The dipolar dark matter density contrast is suppressed due to weak clustering, ensuring $\sigma \ll \rho_{\text{b}}$, so the galaxy appears predominantly baryonic in MOND fits.
• The polarization field $\bm{\Pi}_{\perp}$ aligns with the gravitational field $\bm{g}$ in static equilibrium, leading to the MOND-like susceptibility $\chi(g) = -1 + \frac{g}{a_0} + \mathcal{O}(g^2)$.
• The model reduces to the $\Lambda$-CDM scenario at early cosmological times, validating its consistency with large-scale structure formation.
• The cosmological constant $\Lambda$ is derived to scale as $\Lambda \sim a_0^2$, in excellent agreement with observational constraints.
• The model avoids issues with light deflection, as it maintains standard general relativistic coupling to gravity, preserving predictions for gravitational lensing.