Cyclic Multiverse 朴云松中国科学院研究生院

Cyclic Universe Tolman 1934

”Cyclic multiverse” The number of independent universes increases cycle by cycle. there are lots of independent universes in each cycle or each spacelike slice. Cyclic Universe There is only single universe in each cycle or each spacelike slice.

The perturbation in collapse phase The spectrum of primordial perturbation can be scale Invariant during contraction. Starobinsky 1979, Wands 1999, Steinhardt, Turok et.al 2001 However, different from that in inflation, the amplitude of perturbation modes are increased after their leaving the horizon.

The perturbation in collapse phase The reason is D is the constant mode S is the increasing mode for

expansion contraction Piao, Zhang, PRD70, (2004) On the generation of primordial perturbation

inflation Steinhardt, Turok Starobinsky, WandsPiao, PRD68, (2003)

Steinhardt, Turok et.al (01) Starobinsky (79), Wands (99)

The perturbation in collapse phase

The perturbation in cyclic universe perturbation modes

The perturbation in collapse phase Piao, PLB677, 1 (2009)

The perturbation in cyclic universe Piao, PLB677, 1 (2009)

The numerical results J. Zhang, Piao, in preparation

The perturbation in cyclic universe Thus in general, after several cycle, on super horizon scale In this case, it is obviously impossible that the different regions of global universe will evolve synchronously, even if they are synchronous in previous cycle.

The perturbation in cyclic universe if a region with super horizon scale has the density perturbation on corresponding scale larger than 1, such a region will correspond to a separated close universe. Carr, Hawking, 1974 The separate universe method for large scale curvature perturbation Wands, Malik, Lyth, Liddle 2000

The perturbation in cyclic universe J. Zhang, Piao, in preparation

The cyclic miltiverse Thus the global universe after several cycles will be inevitably separated into many different parts, each of which actually corresponds to a new universe and will evolve independently of one another, up to separation again.

However, in these case, the universe will be possibly split into smaller and smaller fragments, which will renders the cycle ultimately. The cyclic miltiverse

Design of a cyclic miltiverse inflation period inflation

Design of a cyclic miltiverse dark energy period

Design of a cyclic miltiverse Penrose Diagram Piao, arXiv: arXiv:

Summary 1. The super large scale structure of cyclic universe is generally not homogeneous, the reason is that perturbation on super horizon scale is increased during the contraction of each cycle. 2. Thus the global universe after several cycles will be inevitably separated into many different ``universe”, each of them evolves independently. This leads to a cyclic multiverse scenario. 3. In principle, the implementing of cyclic multiverse requires a period of accelerated expansion, which might provide an alternative motivation for the existence of dark energy.

Thank You !