Induced Phantom and 5D Attractor Solution in Space-Time-Matter Theory

In Spacetime-Matter theory we assume that the 4D induced matter of the $5D$ Ricci-flat bouncing cosmological solutions contains a perfect fluid as well as an induced scalar field. Then we show that the conventional 4D quintessence and phantom models of dark energy could be recovered from the $5D$ cosmological solutions. By using the phase-plane analysis to study the stability of evolution of the $5D$ models, we find that the conventional 4D late-time attractor solution is also recovered. This attractor solution shows that the scale factors of the phantom dominated universes in both the 4D and $5D$ theories will reach infinity in a finite time and the universes will be ended at a new kind of spacetime singularity at which everything will be annihilated. We also find that the repulsive force of the phantom may provide us with a mechanics to explain the bounce.