Ghost condensate model of flat rotation curves

Abstract

An effective action of ghost condensate with higher derivatives creates a source of gravity and mimics a dark matter in spiral galaxies. We present a spherically symmetric static solution of Einstein--Hilbert equations with the ghost condensate at large distances, where flat rotation curves are reproduced in leading order over small ratio of two energy scales characterizing constant temporal and spatial derivatives of ghost field: $μ_*^2$ and $μ_\star^2$, respectively, with a hierarchy $μ_\star\ll μ_*$. We assume that a mechanism of hierarchy is provided by a global monopole in the center of galaxy. An estimate based on the solution and observed velocities of rotations in the asymptotic region of flatness, gives $μ_*\sim 10^{19}$ GeV and the monopole scale in a GUT range $μ_\star\sim 10^{16}$ GeV, while a velocity of rotation $v_0$ is determined by the ratio: $ \sqrt{2} v_0^2= μ_\star^2/μ_*^2$. A critical acceleration is introduced and naturally evaluated of the order of Hubble rate, that represents the Milgrom's acceleration.