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Starting the Universe: Stable violation of the Null Energy Condition and Non-Standard Cosmologies. hep-th/0606090 Leonardo Senatore (Harvard) With P.Creminelli, M. A. Luty, A. Nicolis. Outline. Motivation: Today’s Acceleration and Alternative Cosmologies

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Starting the Universe:Stable violation of the Null Energy Conditionand Non-Standard Cosmologies

hep-th/0606090

Leonardo Senatore (Harvard)

With P.Creminelli, M. A. Luty, A. Nicolis


Outline
Outline

  • Motivation: Today’s 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


Motivation

  • Today’s 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


Why nec
Why NEC ?

  • NEC: for every null .

  • With :

  • Singularity Theorems (Borde and Vilenkin)


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.


  • 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


    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


    FRW goldstone effective action

    • Write all the relevant terms:

    • Dispersion relation:

    • Instability for: ,

    • Cured for:


    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


    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


    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

    • Today’s acceleration with :


    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:


    Ever Expanding Cyclic Universe

    • Connect today’s acceleration with past inflation.

    • Model always stable

    • Observational signatures

      • Tilt of Power Spectrum

      • Gravity wave with Blue tilt



    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


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