Fate of bound systems in phantom and quintessence cosmologies

Abstract

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.[1] that bound structures get dissociated in phantom cosmologies but we demonstrate that this happens earlier than anticipated in Ref. [1]. 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 (ρ + 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 in [1] for a phantom cosmology with w=-1.5. A numerical reconstruction of the dissociating bound orbits is presented.

Evolution of gravitational orbits in the expanding universe

“…The acceleration of the scale factor increases towards a singularity which is characterized by the divergences of the scale factor, the Hubble parameter H and its derivativeḢ and the scalar curvature [17]. The repulsive gravitational action of the phantom energy will overcome the normal binding force of structures which will get dissociated [16,17]. As for the case −1/3 < w X0 < −1, the perturbation is positive at late time, but both the perturbation,R/R, and the rate of change of the perturbation, d(R/R)/dt, grow with time.…”

“…the age of the universe. Equation (5) can be conveniently rewritten in cylindrical coordinates {x, ϕ} [5,16]. For a test particle around a massive central object M , it is…”

“…In the phantom scenario, the orbit radius will eventually diverge. Then, the perturbation approach is not enough to track the complete evolution of the system, but alternative analytical methods can be used [10,16]. The dynamics of the radial motion of the bound system can be seen as determined by an effective potential.…”

Confronting quintessence models with recent high-redshift supernovae data

“…Thus for instance, it is known that the Gold dataset [1] prefers models with w X < ÿ1 [17,18], the so called phantom dark energy models, whereas for the more recent Supernova Legacy Survey (SNLS) [2], the best fit is closer to a pure cosmological constant [19,20]. Therefore it is worth exploring what kind of constraints are imposed in each case, and this is the aim of the present work.…”

“…We have marginalized 2 over all values ofM by expanding and minimizing (12) with respect toM (see [16,17,19]). …”