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Cyclic Universe

Tolman 1934

Cyclic Universe

There is only single universe in each cycle

or each spacelike slice.

”Cyclic multiverse”

The number of independent universes increases cycle by cycle.

there are lots of independent universes 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.

On the generation of primordial perturbation

inflation

Steinhardt,

Turok

Piao, PRD68, 083515 (2003)

Starobinsky, Wands

Steinhardt, Turok et.al (01)

Starobinsky (79), Wands (99)

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.

The cyclic miltiverse

However, in these case, the universe will

be possibly split into smaller and smaller fragments, which will renders the cycle ultimately.

Design of a cyclic miltiverse

dark energy period

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.

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