The Equivalence Principle and the Emergence of Flat Rotation Curves

We explain flat rotation curves and the baryonic Tully-Fisher relation by a combination of three hypotheses. The first is a formulation of the equivalence principle for gravitationally bound quantum $N$ body systems, while the second is a second order phase transition hypothesized to arise from a competition between the effects of Unruh and deSitter radiation experienced by a static observer in a galaxy. The third is a light dark matter particle, coupled to a dark photon. The phase transition is triggered in a ring where the Unruh temperature of a static observer falls below the deSitter temperature, thus explaining the apparent coincidence that Milgrom's $a_0 \approx a_\Lambda = c^2 \sqrt{\frac{\Lambda}{3}}$ This phase transition drives the dark matter particles to a regime characterized by a broken $U(1)$ invariance and an approximate scale invariance. In this regime, the dark matter condenses to a super-current characterized by a differentially rotating ring with a flat rotation curve, coupled to a dark magnetic field. The baryonic Tully Fisher relation is a direct consequence of the approximate scale invariance.