1. Inflation and Branes Bottom-up approach to inflation: reconstruction of acceleration trajectories Top-down approach to inflation: seeks to embed it in fundamental theory Lev Kofman, CITA Nearly Normal Galaxies August 8, 2005, Santa Cruz

2. Early Universe Inflation Scale factor time Realization of Inflation

3. Particlegenesis time Inflation no entropy no temperature BANG

5. Classical Quantum Decay of inflaton and preheating after inflation movie Felder, LK, Linde, 01,05

6. Classical Quantum Decay of inflaton and preheating after inflation

7. inflation Hot FRW Initial conditions from Inflation

8. 4 dimensional Inflation predicts No classical inhomogeneities from the past Scale free gaussian fluctuations of all light scalars No vector perturbations Scalar (almost scale free gaussian) metric perturbations Tensor (scale free gaussian) metric perturbations Creation of all SM particles in preheating/thermalization

9. Inflation in the context of ever changing fundamental theory 1980 2000 1990 -inflationOld Inflation New Inflation Chaotic inflation Double Inflation Extended inflation DBI inflation Super-natural Inflation Hybrid inflation SUGRA inflation SUSY F-term inflation SUSY D-term inflation SUSY P-term inflation Brane inflation K-flation N-flation Warped Brane inflation inflation Power-law inflation Tachyon inflation Racetrack inflation Assisted inflation

10. Search for inflaton with branes in extra dimensions 4-dim picture Dvali,Tye 98

11. Compactification of inner dimensions with branes Old string theory New phenomenology Strongly warped 5d geometry Randal, Sundrum 99

12. New ideas about 4d gravity New interactions with SM particles New ideas about mass hierarchy New ideas about cosmological constant New ideas about Inflation

13. Stabilization of Inner dimensions and moduli in string theory

15. Realization of String Theory Inflation on the ground of KKLT throat warped geometry Hybrid inflation with inflaton fluctuations Mobile brane modulated fluctuations Conformal coupling problem Chaotic inflation scalar field associated with angular position at KKLMMT03 Mukohyama, LK 05 Kallosh etal 02

16. Open strings between branes are unstable End point of inflation BANG SM particles Closed strings Unstable KK modes Long-living KK modes related to inner isometries LK, Yi 05

17. string theorist CY AdS 3+1 FRW Fluctuations in Cosmology with Compactification

18. string theorist CY AdS 3+1 FRW Fluctuations in Cosmology with Compactification CY cosmologist

19. string theorist Practical cosmologist CY AdS CY +fluctuations 3+1 FRW 3+1 FRW +fluctuations Fluctuations in Cosmology with Compactification CY cosmologist

20. Modulated Fluctuations Light field at inflation Inflation radiation LK03, Dvali etal03

21. 4 dim Inflation in 10dim String Theory predicts All what 4 dim inflation predicts Scale free gaussian fluctuations of many light scalars Creation of non-SM particles (KK modes) in reheating/thermalization Short-wavelength gravitational radiation Modulated cosmological fluctuations String theory Cosmic strings

22. Scanning Inflation R.Bond, C.Contaldi, A.Frolov, L.Kofman T.Souradeep P.Vandrevange Bottom-up

24. Inflation in the context of ever changing fundamental theory 1980 2000 1990 -inflationOld Inflation New Inflation Chaotic inflation Double Inflation Extended inflation DBI inflation Super-natural Inflation Hybrid inflation SUGRA inflation SUSY F-term inflation SUSY D-term inflation SUSY P-term inflation Brane inflation K-flation N-flation Warped Brane inflation inflation Power-law inflation Tachyon inflation Racetrack inflation Assisted inflation

25. Ensemble of Inflationary trajectories Chebyshev decomposition Space of models opens wide

27. Observational constraints on trajectories Markov Chain Monte Carlo

28. Degeneracy of the Potential Reconstruction

29. Reconstruction of Inflationary Trajectory

30. Cosmic Numerology: CMBall + LSS, stable & consistent pre-WMAP1 & post- WMAP1 (BCP03), Jun03 data (BCLP04), CMBall+CBIpol04, CMBall+Boom03+LSS Jul’21 05, CMBall Jul05 LSS=2dF, SDSS (weak lensing, cluster abundances); also HST, SN1a A s = 22 +- 3 x 10 -10 n s =.95 +-.02 (.97 +-.02 with tensor) (+-.004 PL1) A t / A s < 0.36 95% CL (+-.02 PL2.5+Spider) dn s /dln k = -.07 +-.04 to -.05 +-.03 (+-.005 P1) -.002 +-.01 (+Lya McDonald etal 04) (A iso / A s < 0.3 large scale, < 3 small scale n iso = 1.1+-.6) The Parameters of Cosmic Structur Formation