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W. Kinney - Scale-Invariant Perturbations: is Inflation the only Way?


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The SEENET-MTP Workshop BW2011
Particle Physics from TeV to Plank Scale
28 August – 1 September 2011, Donji Milanovac, Serbia

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W. Kinney - Scale-Invariant Perturbations: is Inflation the only Way?

  1. 1. Inflation … Or What? Will Kinney Seenet­MTP Workshop Balkan Summer Institute, Donji Milanovac  31 August 2011  
  2. 2. CMB: Basic Properties Adiabatic density perturbations Superhorizon correlations Gaussian statistics Near scale­invariance over a factor of 1000 in wavelength Q: What does this really tell us?   
  3. 3. Generation of Perturbations Horizon Mode freezing   
  4. 4. Generation of Perturbations Comoving horizon: Decelerating Expansion: Accelerating Expansion: Key ingredient for generation of perturbations:  shrinking horizon   
  5. 5. The Comoving Horizon in Inflation Decelerating Accelerating   
  6. 6. The Comoving Horizon in Inflation   
  7. 7. Mode Exit and Re­entry re­entry classical exit quantum   
  8. 8. Larger Scales Exit Earlier   
  9. 9. Superhorizon Perturbations   
  10. 10. The Horizon Is Not The Horizon The Hubble length is not the causal horizon in inflation. Mode freezing has absolutely nothing to do with causality.   
  11. 11. The Horizon Is Not The Horizon In general, the Hubble length is not even the freezeout horizon: Scale invariance and freezeout:   
  12. 12. Is Inflation the Only Way? Comoving Horizon  (constant equation of state): Decelerating Expansion: Accelerating Expansion: Duality:    (Boyle, et al., hep­th/0403026)
  13. 13. The Comoving Hubble Horizon in Inflation Decelerating Accelerating   
  14. 14. The Comoving Hubble Horizon in Bouncing Cosmology Expansion Bounce Contraction   
  15. 15. The Cyclic Dual to Slow Roll Slow Roll   
  16. 16. The Cyclic Dual to Slow Roll Slow Roll   
  17. 17. The Cyclic Dual to Slow Roll Slow Roll Dual­Slow Roll Quasi­static contraction   
  18. 18. Perturbations Slow Roll Dual­Slow Roll  (WHK, Moradinezhad Dizgah, arXiv:1007.0753)  
  19. 19. Ekpyrosis: Problems Shrinking proper Hubble length:  blue spectra Instabilities: growing mode Negative potential Singular bounce Name sounds like a skin disease Buchbinder, Khoury & Ovru, PRD 76, 123503 (2007) Khoury & Steinhardt, arXiv:0910.2230 Linde, Mukhanov & Vikman, arXiv:0912.0944   
  20. 20. Generating Superhorizon Perturbations New result: In an expanding universe, to generate  perturbations consistent with observation, you must have one of: (1) Accelerated Expansion (2) Superluminal Sound Speed (3) Super­Planckian Energy Density    (Geshnizjani, WHK, Moradinezhad Dizgah, arXiv:1107.1241)
  21. 21. Non­Canonical Lagrangians as Bimetric Theories Lagrangian with arbitrary kinetic term: Acoustic metric Light cone:  Two horizons! Acoustic cone:    
  22. 22. Light Cones in DBI Inflation  Acoustic Cone: Light cone: x y   
  23. 23. Mode Freezing and Horizons Tensor modes freeze out at the Hubble Horizon Scalar modes freeze out at the Acoustic Horizon Curvature perturbations generated by shrinking acoustic horizon!    (Garriga & Mukhanov, arXiv:hep­th/9904176)
  24. 24. Horizons in DBI Inflation Hubble Horizon  Acoustic Horizon   
  25. 25. Beyond Inflation For               we still need inflation to generate superhorizon perturbations. Tachyacoustic Cosmology : generate superhorizon perturbations in a   radiation­ or matter­dominated universe Armendariz­Picon, arXiv:astro­ph/0606168 Piao, arXiv:gr­qc/0609071 Magueijo, arXiv:08030859 Bessada, WHK, Stojkovic, Wang, arXiv:0908.3898 Causally self­consistent cosmology: no timelike loops. Babichev, Mukhanov & Vikman, arXiv:0708.0561   
  26. 26. Light Cones in Tachyacoustic Cosmology  Acoustic Cone: Light cone: x y   
  27. 27. The Tachyacoustic Solution Decelerating Expansion: Decaying Sound Speed:   
  28. 28. Horizons in Tachyacoustic Cosmology Hubble Horizon: Acoustic Horizon: Hubble Horizon grows  (no tensor modes!) Acoustic Horizon shrinks   
  29. 29. Horizons in Tachyacoustic Cosmology Hubble Horizon  Acoustic Horizon   
  30. 30. Perturbations in Tachyacoustic Cosmology Hubble Horizon: Acoustic Horizon: (Magueijo, arXiv:0803.0859)    (Bessada, WHK, Stojkovic, Wang, arXiv:0908.3898)
  31. 31. Tachyacoustic Cosmology: Problems String embedding problematic Does not solve flatness problem Initial singularity Is it a dynamical attractor?  (Preliminary: yes)   
  32. 32. Summary The Hubble length is not the horizon. Expanding universe: only three ways to get scale invariance for a sufficient range of super­Hubble  perturbations: Accelerated expansion Superluminal sound speed Transplanckian energy density Nothing works nearly as well as inflation.