We study analytically and numerically the evolution of bound systems in universes with accelerating expansion where the acceleration either increases with time towards a Big Rip singularity (phantom cosmologies) or decreases with time (quintessence). We confirm the finding of Caldwell et. al.
[arXiv:astro-ph/0302506] (hereafter CKW) that bound structures get dissociated in phantom cosmologies but we demonstrate that this happens earlier than anticipated by CKW. In particular we find that the `rip time' when a bound system gets unbounded is not the time when the repulsive phantom energy gravitational potential due to the average (r+ 3p) balances the attractive gravitational potential of the mass M of the system. Instead, the `rip time' is the time when the minimum of the time dependent effective potential (including the centrifugal term) disappears. For the Milky Way galaxy this happens approximately 180Myrs before the Big Rip singularity instead of approximately 60Myrs indicated by CKW for a phantom cosmology with w=-1.5. A numerical reconstruction of the dissociating bound orbits is presented.
 

The Dissociation of a Milky Way scale System 
in a Phantom Cosmology (w=-1.2)

Numerical Analysis

The file figures-br.nb has been used for the construction of the figures of the paper. An animation of the dissociating orbit has been included at the end of the file. Constructed with Mathematica 4.1.

Download  the mathematica file figures-br.nb (compressed form)

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