Dark Energy and the Return of the Phoenix Universe

Abstract

In cyclic universe models based on a single scalar field (e.g., the radion determining the distance between branes in M-theory), virtually the entire universe makes it through the ekpyrotic smoothing and flattening phase, bounces, and enters a new epoch of expansion and cooling. This stable evolution cannot occur, however, if scale-invariant curvature perturbations are produced by the entropic mechanism because it requires two scalar fields (e.g., the radion and the Calabi-Yau dilaton) evolving along an unstable classical trajectory. In fact, we show here that an overwhelming fraction of the universe fails to make it through the ekpyrotic phase; nevertheless, a sufficient volume survives and cycling continues forever provided the dark energy phase of the cycle lasts long enough, of order a trillion years. Two consequences are a new role for dark energy and a global structure of the universe radically different from that of eternal inflation.

Figures (3)

• Figure 1: This figure shows the evolution of adjacent classical trajectories from the ekpyrotic phase through a kinetic phase to the big crunch. The trajectories get reflected by a boundary in scalar field space at $\phi_2=0.$ All times are in units of the Planck time.
• Figure 2: After the big bang, adjacent trajectories proceed through a second kinetic phase and roll back up the ekpyrotic potential, where the radiation dominated phase starts at $t\approx 10^{15}$ Planck times. During the ensuing matter and dark energy phases, the scalar fields remain almost immobile.
• Figure 3: The global structure of the two- field cyclic universe: large smooth and flat regions are interspersed with small regions that have collapsed and have stopped cycling. The tiny regions of lighter shade will turn into the entire habitable regions during the next cycle.