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The Games for Universe. Yun-Song Piao Interdisciplinary Center of Theoretical Studies Chinese Academy of Sciences. Some of Rceent Works Piao, hep-th/0407258, Can Universe Experience Many Cycles with Different Vacua ?

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The Games for Universe

Yun-Song Piao

Interdisciplinary Center of Theoretical Studies

Chinese Academy of Sciences


Some of Rceent Works

Piao, hep-th/0407258,

Can Universe Experience Many Cycles with

Different Vacua ?

accepted in Phys.Rev.D (Rapid Communication)

Piao, Feng, Zhang, hep-th/0310206,

Suppressing CMB Quadrupole with a Bounce from

Contracting Phase to Inflation

Phys.Rev.D69 103520(2004)

Piao, gr-qc/0410206

Preheating and Dark Sector of Universe


The notion that the number of vacua is astronomical

  • has received much attentions, recently
  • 1) String Theory
  • 2) Explaining Observation
  • The dynamical mechanism
  • (might select some in which we live)
  • Eternal Inflation
  • various regions (bubbles) with different vacua
  • Other ?
  • for example, various periods (cycles) with
  • different vacua

It is wellknown that

1) For an expanding universe with dS minimum, it will arrive at a dS regime symptotically.

2) The universe with AdS minimum can not approach an AdS regime, and instead it will stop expanding and enter into a collapsing phase. During the collapsing process, its energy goes up rapidly. The singularity will become inevitable unless there is a mechanism responsible for the bounce.

3) When the universe is in the contracting phase, the field can be driven and roll up along its potential, and arrive at a large enough value for asuccessful inflation to occur in expanding phase for a feasible bounce.


The potential for our purpose

When the field rolls down to the minima of its potential, the universe will collapse eventually. In the minima of potential

The anti-frictional term can be neglected.

The motion of equation becomes

whose solution is


When the anti-frictional term can be not neglected any

more, the oscillations of field ends. The universe enters

into the regime dominated by kinetic energy.

In high energy regime, we take for the bounce

During a cycle, the change of field value is approximately

When the anti-frictional term can be not neglected any more


Some Comments

  • The efficience of cycle
  • 2) If cycle is efficient, when the number of cycles is large or approaches infinity, whichever minima is initially in, it can run over almost all minima of potential.
  • 3) If there is a final theory where some vacua suitable us exist, there are certainly some cycles in which we can live.
  • 4) In this sense, the universe with a early successful inflation and a late time small cosmological constant may be anthropic one of many cycles.

Matching CMB Observation

The connection between different vacua provides a

suppression of scalar perturbation spectrum on large scale

For kinetic dominated and potential dominated phase

after matching background


The equation of scalar perturbation

For kinetic dominated phase

For inflation phase


Taking the potential as

Considering a coupe to a massive field

When phi field crosses the oringin, the occupation number

of chi particles suddenly acquire the value


The number density of chi particles is approximately

The density of dark energy is about the same as dark energy’s

at present requires

Making phi stay in a false vacumm up to today requires


The comoving free streaming scale for nonthermal

produced particles is

which requiresi



  • The universe can experience many cycles with different
  • vacua, under certain conditions.
  • 2) The connection between two different vacua may give a
  • possible explanation to the suppression of power spectrum
  • on large scale,
  • 3) The production of light particles may make the universe
  • stay in some state with very long time.
  • Further, there might few vacua satisfying such conditions,
  • in which dark matter produced during preheating can trap us
  • in a cycle dominated by dark energy at late time.