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hep-th/0606090 Leonardo Senatore (Harvard) With P.Creminelli, M. A. Luty, A. Nicolis

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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hep-th/0606090 Leonardo Senatore (Harvard) With P.Creminelli, M. A. Luty, A. Nicolis

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  1. 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

  2. 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

  3. 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

  4. Why NEC ? • NEC: for every null . • With : • Singularity Theorems (Borde and Vilenkin)

  5. 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.

  6. 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

  7. 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

  8. FRW goldstone effective action • Write all the relevant terms: • Dispersion relation: • Instability for: , • Cured for:

  9. 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

  10. 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

  11. 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 :

  12. 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:

  13. 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

  14. The Big Bounce

  15. 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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