Limits on nonGaussianities from WMAP data

1
Starting the UniverseStable violation of
the Null Energy Conditionand Non-Standard
Cosmologies
hep-th/0606090 Leonardo Senatore
(Harvard) With P.Creminelli, M. A. Luty, A.
Nicolis
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Outline

• Motivation Todays Acceleration and Alternative
  Cosmologies
• Necessity to violate the Null Energy Condition
  (NEC)
• Our Approach to the Problem and its Solution
• Examples of Alternative Cosmologies
• Conclusions

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Motivation

• Todays acceleration ?
  ?
• Alternative Cosmologies
• Inflation has singularity in the past
• Avoid it
• Start the Universe in the past
• Bouncing Cosmology from contraction to
  expansion
• Cyclic Universe
• All these require NEC violation to have

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Why NEC ?

• NEC for every null
  .
• With
• Singularity Theorems (Borde and Vilenkin)

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Energy Conditions

• Assumptions, not Deductions
• Most are violated
• Strong
  for timelike
• Weak
  for timelike
• Are violated by the C.C.
• But NEC is hard instabilities appear
• S.Dubovsky, T.Gregoise, A.Nicolis, R.Rattazzi,
• S.D.H.Hsu, A.Jenkins, M.B. Wise,
• Phantom fields.
• Question does NEC really holds in Cosmology?
• We will see the answer is NO.

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Our Approach

• Question can NEC be violated?
• Build general low energy EFT for FRW background
  how?
• Action for the Goldstone of spontaneously broken
  time diffeomorphisms.
• This is the relevant fluctuation inside the
  horizon

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How to build it?

• Go to a unitary gauge where
• Fluctuation inside the metric.
• Write action withall terms compatible with
  residual gauge inv. Ex.
• Reintroduce Goldstone
• Gauge invariant combination
• Concentrate on the action

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FRW goldstone effective action

• Write all the relevant terms
• Dispersion relation
• Instability for ,
• Cured for

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Mixing with Gravity

• Usually negligible inside the horizon
• The higher derivative terms mix more strongly
• Jeans-like instability
• Final parametric range for stable NEC violation

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Applications

• Possibility that today. From WMAP
  
• New possibilities for the Early Universe
• Starting the Universe in the
  past.
• Eternally expanding cyclic universe
• The Big Bounce

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Tilted Ghost Condensation

• Ghost Condensation
• (N.
  Arkani-Hamed, H.C. Cheng, M.A.Luty,S. Mukohyama)
• 
  (N. Arkani-Hamed, P.
  Creminelli, S.Mukohyama, M.Zaldarriaga)
• 
  (L.
  Senatore)
• Add a tilt
• Todays acceleration with

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Starting the Universe

• No Big Bang in the past.
• Ghost condensate with
• In the past the Cosmology is
• Need to ensure stability in the past

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Ever Expanding Cyclic Universe

• Connect todays acceleration with past inflation.
• Model always stable
• Observational signatures
• Tilt of Power Spectrum
• Gravity wave with Blue tilt

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The Big Bounce
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Conclusions

• No Obstacle to violating NEC at EFT level
• Models with are now
  conceivable
• Two Instabilities
• Gradient Instability Higher
  derivative terms
• Jeans Instability
• Safe for (parametrically for
  )
• Examples of Alternative Cosmologies
• today
• Starting the Universe in the
  past.
• Cyclic Ever Expanding Universe
• Bouncing Universe
• Open questions and future work
• More degrees of freedom stronger NEC
  violation?
• Realistic and predictive Cosmological Models
• UV completion