Milgrom's Law and Lambda's Shadow: How Massive Gravity Connects Galactic and Cosmic Dynamics

TL;DR

This paper proposes that massive gravity theories can naturally explain galactic dynamics without dark matter and connect the observed acceleration scale to cosmological parameters, potentially unifying dark matter and dark energy explanations.

Contribution

It demonstrates a derivation linking Milgrom's law acceleration constant to cosmological parameters within massive gravity frameworks, suggesting a unified explanation for dark matter and dark energy.

Findings

Milgrom's constant derived from cosmological parameters

Massive gravity can reproduce modified Newtonian dynamics

Potential unification of dark matter and dark energy explanations

Abstract

Massive gravity provides a natural solution for the dark energy problem of cosmology and is also a candidate for resolving the dark matter problem. I demonstrate that, assuming reasonable scaling relations, massive gravity can provide for Milgrom's law of gravity (or "modified Newtonian dynamics") which is known to remove the need for particle dark matter from galactic dynamics. Milgrom's law comes with a characteristic acceleration, Milgrom's constant, which is observationally constrained to $a_0\approx1.1\times10^{-10}$ m/s$^2$. In the derivation presented here, this constant arises naturally from the cosmologically required mass of gravitons like $a_0\propto c\sqrt{\Lambda}\propto c H_0\sqrt{3\Omega_{\Lambda}}$, with $\Lambda$, $H_0$, and $\Omega_{\Lambda}$ being the cosmological constant, the Hubble constant, and the third cosmological parameter, respectively. My derivation suggests that massive gravity could be the mechanism behind both, dark matter and dark energy.