MOND from a brane-world picture

TL;DR

This paper proposes a heuristic brane-world model where Modified Newtonian Dynamics (MOND) naturally emerge from geometric properties of a nearly spherical brane embedded in higher-dimensional space, linking MOND to cosmology and gravity.

Contribution

It introduces a novel geometric brane-world framework that explains MOND phenomena and explores implications for cosmology and the transition to relativistic gravity.

Findings

MOND acceleration scale linked to brane tension and geometry

Emergence of MOND dynamics from brane perturbations

Potential dependence of a_0 on cosmological parameters

Abstract

I describe a heuristic model where MOND dynamics emerge in a universe viewed as a nearly spherical brane embedded in a higher-dimensional flat space. The brane, described by $\xi(\Omega)$, is of density $\sigma$ ($\xi$ and $\Omega$ are the radial and angular coordinates in the embedding space). The brane and matter -- confined to the brane and of density $\rho(\Omega)\ll\sigma$ -- are coupled to a potential $\varepsilon(\xi)$. I restrict myself to shallow perturbations, $\xi(\Omega)=\ell_0+\zeta(\Omega)$, $|\zeta|\ll\ell_0$. A balanced brane implies $\hat a_0\equiv\varepsilon'(\ell_0)\sim T/\sigma\ell_0$, $T$ is the brane tension, yielding for the velocity of small brane perturbations $c^2\sim T/\sigma\sim \ell_0\hat a_0$. But, $\hat a_0$ plays the role of the MOND acceleration constant in local gravitational dynamics; so $\hat a_0\sim c^2/\ell_0$. What we, in the brane, perceive as the gravitational potential is $\phi\equiv\varepsilon[\xi(\Omega)]\approx \phi_0+\hat a_0\zeta$. Aspects of MOND that may emerge naturally as geometrical properties are: a. The special role of acceleration in MOND, and why it is an acceleration, $a_0$, that marks the transition from the standard dynamics much above $a_0$ to scale-invariant dynamics much below $a_0$. b. The intriguing connection of $a_0$ with cosmology. c. The Newtonian limit corresponds to local departure $|\zeta|\ll\ell_0$; i.e., $\phi-\phi_0\sim a_0\zeta\ll a_0\ell_0\sim c^2$ - whereas relativity enters when $|\zeta|\not\ll\ell_0$. The model also opens new vistas for extension, e.g., it points to possible dependence of $a_0$ on $\phi$, and to $a_0$ losing its status and meaning altogether in the relativistic regime. The required global balance of the brane might solve the `old' cosmological-constant problem. I discuss possible connections with the nearly-de-Sitter nature of our Universe. (Abridged.)