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The evolution of a bound system in the expanding background has beeninvestigated in this paper. The background is described by a FRW universe withthe modified holographic dark energy model, whose equation of state parameterchanges with time and can cross the phantom boundary. To study the evolution ofthe bound system, an interpolating metric is considered, and on this basis thegeodesics of a test particle are given. The equation of motion and theeffective potential are also derived from the geodesics. By studying the theeffective potential and the evolution of the radius of a test particle in thebound system of the Milky Way galaxy, we have found that the galaxy would gothrough three stages: expands from a singular point; stays in a discoid for aperiod of time; big rip in the future. With the help of analysing the criticalangular momentum, we find that the test particle needs less angular momentum toescape from the center mass as time passes.

A bound system in the expanding universe with modified holographic Ricci dark energy and dark matter