Scaling Dark Energy in a Five-Dimensional Bouncing Cosmological Model

Abstract

We consider a 5-dimensional Ricci flat bouncing cosmological model in which the 4-dimensional induced matter contains two components at late times - the cold dark matter (CDM)+baryons and dark energy. We find that the arbitrary function $f(z)$ contained in the solution plays a similar role as the potential $V(\varphi )$ in quintessence and phantom dark energy models. To resolve the coincidence problem, it is generally believed that there is a scaling stage in the evolution of the universe. We analyze the condition for this stage and show that a hyperbolic form of the function $f(z)$ can work well in this property. We find that during the scaling stage (before $z\approx 2$), the dark energy behaves like (but not identical to) a cold dark matter with an adiabatic sound speed $c_s^2\approx 0$ and $p_x\approx 0$. After $z\approx 2$, the pressure of dark energy becomes negative. The transition from deceleration to acceleration happens at $z_T\approx 0.8$ which, as well as other predictions of the $5D$ model, agree with current observations.

13 pages, 1 table, 3 figures, published version, references added