1. Surveying Inflation and Reheating Cosmological Landscape: Strings, Gravity and Inflation Seoul, September 2005 “K. listened intently. So the Castle had appointed him land surveyor …” “The Castle” by F.Kafka Lev Kofman, CITA

2. Bottom-up approach to inflation: reconstruction of acceleration trajectories Top-down approach to inflation: seeks to embed it in fundamental theory

3. Early Universe Inflation Scale factor time Realization of Inflation

4. Phase portrait of inflation

5. Particlegenesis time Inflation no entropy no temperature BANG

7. Occupation number Classical Quantum Resonant Preheating in Chaotic Inflation

9. Classical Quantum Decay of inflaton and preheating after inflation movie Felder, LK,05

10. Classical Quantum Decay of inflaton and preheating after inflation

11. Tachyonic Preheating in Hybrid Inflation l movie Felder, LK, Linde,01

12. Tachyonic Preheating

14. inflation Hot FRW Initial conditions from Inflation

15. Modulated Fluctuations Light field at inflation Inflation radiation LK03;Dvali et al,03

16. Modulated fluctuations in Chaotic Inflation Podolsky, Felder, LK,Peloso hep-ph/0507096

17. Modulated fluctuations in Hybrid Inflation inhomogeneous waterfall

18. Bernardeau, Uzan, LK 03

19. 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 One inflation helps to ignite another inflation

20. 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

21. Search for inflaton with branes in extra dimensions 4-dim picture Dvali,Tye 98 Prototype of hybrid inflation

22. Compactification of inner dimensions with branes Old string theory New phenomenology Strongly warped 5d geometry RS 99

23. Stabilization of Inner dimensions and moduli in string theory

25. Realization of String Theory Chaotic Inflation Mobile brane Chaotic inflation

26. Realization of String Theory Inflation on the ground of KKLT throat warped geometry Mobile brane modulated fluctuations Conformal coupling problem scalar field associated with angular position at KKLMMT03 Warped brane inflation Realization of warped brane inflation with conformal inflaton

27. Reheating after String Theory Inflation Barnaby, Burgess, Cline, hep-th/0412095 LK, Yi, hep-th/0507257 Frey, Mazumdar, Myers, hep-th/0508139 Chialva, Shiu, Underwood, hep-th/0508229

28. 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

30. KK story KK particles are thermalized first SM particles are thermalized much later KK from M with isometries are stable No complete decya KK particles freeze out

31. KK SM

32. 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

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

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

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

36. background fluctuations

38. Fluctuations in Cosmology with Compactification

39. Gravitational instability of anysotropoc geometry

40. Too strong fluxes lead to new instability

41. Summary Theory of cosmological fluctuations in models with extra dimensions Generic properties of fluctuations in 3+1+d dim Instabilities exclude regions of landscape Potential observables: varying couplings/masses, Primordial fluctuations

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

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

46. Observational constraints on trajectories Markov Chain Monte Carlo

47. Degeneracy of the Potential Reconstruction

50. “Best fit” model is awkward: features in the potential suppression of scalar mode at large scales large tensor mode Bottom-up: personal priors Top-down approach: no priors Non-vanishing probability

52. Reconstruction of Inflationary Trajectory