hep-th/ 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

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 Outline

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 Motivation

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

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. Energy Conditions

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 Our Approach

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 How to build it?

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

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

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

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 : Tilted Ghost Condensation

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

Connect today’s acceleration with past inflation. Model always stable Observational signatures –Tilt of Power Spectrum –Gravity wave with Blue tilt Ever Expanding Cyclic Universe

The Big Bounce

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 Conclusions