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

摘要

Massive gravity provides a natural solution for the dark energy problem ofcosmology and is also a candidate for resolving the dark matter problem. Idemonstrate that, assuming reasonable scaling relations, massive gravity canprovide for Milgrom's law of gravity (or "modified Newtonian dynamics") whichis 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 thecosmologically required mass of gravitons like $a_0\proptoc\sqrt{\Lambda}\propto c H_0\sqrt{3\Omega_{\Lambda}}$, with $\Lambda$, $H_0$,and $\Omega_{\Lambda}$ being the cosmological constant, the Hubble constant,and the third cosmological parameter, respectively. My derivation suggests thatmassive gravity could be the mechanism behind both, dark matter and darkenergy.