1. Les Houches Lectures on Cosmic Inflation Four Parts 1)Introductory material 2)Entropy, Tuning and Equilibrium in Cosmology 3)Classical and quantum probabilities in the multiverse 4)de Sitter equilibrium cosmology Andreas Albrecht; UC Davis Les Houches Lectures; July-Aug 2013 1Albrecht Les Houches Lectures 2013 Pt. 4

2. Part 4 Outline 1.de Sitter Equilibrium cosmology 2.Cosmic curvature from de Sitter Equilibrium cosmology Albrecht Les Houches Lectures 2013 Pt. 42

3. Part 4 Outline 1.de Sitter Equilibrium cosmology 2.Cosmic curvature from de Sitter Equilibrium cosmology Albrecht Les Houches Lectures 2013 Pt. 43

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10. 10 AA: arXiv:1104.3315 AA: arXiv:0906.1047 AA & Sorbo: hep-th/0405270

11. Albrecht Les Houches Lectures 2013 Pt. 411 Evolution of Cosmic Length

12. Albrecht Les Houches Lectures 2013 Pt. 412 Evolution of Cosmic Length

13. Albrecht Les Houches Lectures 2013 Pt. 413

14. Albrecht Les Houches Lectures 2013 Pt. 414

15. domination Albrecht Les Houches Lectures 2013 Pt. 415

16. domination Asymptotic behavior  de Sitter Space Albrecht Les Houches Lectures 2013 Pt. 416

17. The de Sitter horizon Past horizon of observation event at this time 17Albrecht Les Houches Lectures 2013 Pt. 4 Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.

18. The de Sitter horizon Past horizon of observation event at this time 18Albrecht Les Houches Lectures 2013 Pt. 4 Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.

19. The de Sitter horizon Past horizon of any observation event deep in the de Sitter era 19Albrecht Les Houches Lectures 2013 Pt. 4 Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.

20. Past horizon of any observation event deep in the de Sitter era Future horizon of event at reheating (distance photon has traveled, in SBB). Albrecht Les Houches Lectures 2013 Pt. 420 Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.

21. Implications of the de Sitter horizon Maximum entropy Gibbons-Hawking Temperature Gibbons & Hawking 1977 Albrecht Les Houches Lectures 2013 Pt. 421

22. “De Sitter Space: The ultimate equilibrium for the universe? Horizon Albrecht Les Houches Lectures 2013 Pt. 422

23. Banks & Fischler & Dyson et al. Implications of the de Sitter horizon Maximum entropy Gibbons-Hawking Temperature Only a finite volume ever observed If is truly constant: Cosmology as fluctuating Eqm. Maximum entropy finite Hilbert space of dimension Albrecht Les Houches Lectures 2013 Pt. 423

24. Banks & Fischler & Dyson et al. Implications of the de Sitter horizon Maximum entropy Gibbons-Hawking Temperature Only a finite volume ever observed If is truly constant: Cosmology as fluctuating Eqm.? Maximum entropy finite Hilbert space of dimension Albrecht Les Houches Lectures 2013 Pt. 424 dSE cosmology

25. Albrecht Les Houches Lectures 2013 Pt. 425 Equilibrium Cosmology

26. Albrecht Les Houches Lectures 2013 Pt. 426 Equilibrium Cosmology  An eqm. theory does not require any theory of initial conditions. The probability of appearing in a given state is given entirely by stat mech, and is thus “given by the dynamics”.  If you know the Hamiltonian you know how to assign probabilities to different states without any special theory of initial conditions. Dyson et al 2002

27. Rare Fluctuation Albrecht Les Houches Lectures 2013 Pt. 427

28. Rare Fluctuation Albrecht Les Houches Lectures 2013 Pt. 428

29. Rare Fluctuation Albrecht Les Houches Lectures 2013 Pt. 429 Move Ergodicity to hidden degrees of freedom (we *know* state counting arguments do note apply to the observable universe) AA in prep

30. Concept: Realization: “de Sitter Space” Albrecht Les Houches Lectures 2013 Pt. 430

31. Rare Fluctuation Albrecht Les Houches Lectures 2013 Pt. 431

32. Albrecht Les Houches Lectures 2013 Pt. 432 Fluctuating from dSE to inflation : The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Farhi-Guth Guven” (FGG) process A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton. Rate is well approximated by the rate of seed formation: Seed mass:

33. Albrecht Les Houches Lectures 2013 Pt. 433 Fluctuating from dSE to inflation : The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Farhi-Guth Guven” (FGG) process A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton. Rate is well approximated by the rate of seed formation: Seed mass: Small seed can produce an entire universe  Evade “Boltzmann Brain” problem

34. Albrecht Les Houches Lectures 2013 Pt. 434 Fluctuating from dSE to inflation : The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Farhi-Guth Guven” (FGG) process A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton. Rate is well approximated by the rate of seed formation: Seed mass: See also Freivogel et al 2006, Banks 2002 M  0 not a problem for G-F process (A. Ulvestad & AA 2012)

35. degrees of freedom temporarily break off to form baby universe: Albrecht Les Houches Lectures 2013 Pt. 435 time Eqm. Seed Fluctuation Tunneling Evolution Inflation Radiation Matter de Sitter Recombination

36. degrees of freedom temporarily break off to form baby universe: Albrecht Les Houches Lectures 2013 Pt. 436 time Eqm. Seed Fluctuation Tunneling Evolution Inflation Radiation Matter de Sitter Recombination “Right Timescale”

37. Albrecht Les Houches Lectures 2013 Pt. 437 Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

38. Albrecht Les Houches Lectures 2013 Pt. 438 Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

39. Albrecht Les Houches Lectures 2013 Pt. 439 Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

40. Albrecht Les Houches Lectures 2013 Pt. 440 This much inflation fills one de Sitter horizon

41. Albrecht Les Houches Lectures 2013 Pt. 441 This much inflation fills more than one de Sitter horizon, generating total entropy and affecting regions beyond the horizon of the observer

42. Albrecht Les Houches Lectures 2013 Pt. 442 In dSE cosmology this region is unphysical. Breakdown of effective field theory prevents inflation from filling more than one de Sitter horizon

43. Albrecht Les Houches Lectures 2013 Pt. 443 In dSE cosmology this region is unphysical. Breakdown of effective field theory prevents inflation from filling more than one de Sitter horizon “Equivalent” to Banks-Fischler holographic constraint on number of e-foldings of inflation (D Phillips & AA in prep)

44. To get eternal inflation, we made what we thought was a simple extrapolation, but wound up with a highly problematic theory Albrecht Les Houches Lectures 2013 Pt. 444 Q

45. dSE: The extrapolation that leads to eternal inflation is naïve, in that it neglects the breakdown of effective field theory. dSE uses holographic arguments to estimate this breakdown. Albrecht Les Houches Lectures 2013 Pt. 445 Q Breakdown of effective field theory (extrapolation invalid)

46. Albrecht Les Houches Lectures 2013 Pt. 446 Fluctuating from dSE to inflation : The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Farhi-Guth Guven” (FGG) process A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton. Rate is well approximated by the rate of seed formation Seed mass: Large exponentially favored  saturation of dSE bound

47. Albrecht Les Houches Lectures 2013 Pt. 447 dSE bound on inflation given by past horizon

48. Albrecht Les Houches Lectures 2013 Pt. 448 dSE bound on inflation given by past horizon A variety of inflation models, all saturating the dSE bound

49. Part 4 Outline 1.de Sitter Equilibrium cosmology 2.Cosmic curvature from de Sitter Equilibrium cosmology Albrecht Les Houches Lectures 2013 Pt. 449

50. Part 4 Outline 1.de Sitter Equilibrium cosmology 2.Cosmic curvature from de Sitter Equilibrium cosmology Albrecht Les Houches Lectures 2013 Pt. 450

51. Friedmann Eqn. Albrecht Les Houches Lectures 2013 Pt. 451

52. Albrecht Les Houches Lectures 2013 Pt. 452 Banks & Fischler & Dyson et al. Evolution of curvature radius

53. Albrecht Les Houches Lectures 2013 Pt. 453 Curvature radius set by initial curvature Banks & Fischler & Dyson et al. Evolution of curvature radius

54. Albrecht Les Houches Lectures 2013 Pt. 454 A variety of inflation models, all saturating the dSE bound Curvature radius set by initial curvature Evolution of curvature radius

55. Albrecht Les Houches Lectures 2013 Pt. 455 A variety of inflation models, all saturating the dSE bound Curvature radius set by initial curvature is given by this gap Evolution of curvature radius

56. Albrecht Les Houches Lectures 2013 Pt. 456 AA: arXiv:1104.3315

57. Albrecht Les Houches Lectures 2013 Pt. 457 dSE Cosmology and cosmic curvature The Guth-Farhi process starts inflation with an initial curvature set by the curvature of the Guth-Farhi bubble Inflation dilutes the curvature, but dSE cosmology has a minimal amount of inflation

58. Albrecht Les Houches Lectures 2013 Pt. 458 Image by Surhud More Predicted from dSE cosmology is: Independent of almost all details of the cosmology Just consistent with current observations Will easily be detected by future observations

59. Albrecht Les Houches Lectures 2013 Pt. 459 Image by Surhud More Predicted from dSE cosmology is: Independent of almost all details of the cosmology Just consistent with current observations Will easily be detected by future observations Work in progress on expected values of (Andrew Ulvestad & AA)

60. Albrecht Les Houches Lectures 2013 Pt. 460 Image by Surhud More Predicted from dSE cosmology is: Independent of almost all details of the cosmology Just consistent with current observations Will easily be detected by future observations Work in progress on expected values of (Andrew Ulvestad & AA)

61. Albrecht Les Houches Lectures 2013 Pt. 461 A variety of inflation models, all saturating the dSE bound Curvature radius set by initial curvature is given by this gap Evolution of curvature radius

62. Albrecht Les Houches Lectures 2013 Pt. 462 Conclusions (Part 4) The search for a “big picture” of the Universe that explains why the region we observe should take this form has proven challenging, but has generated exciting ideas. We know we can do science with the Universe It appears that there is something right about cosmic inflation dSE cosmology offers a finite alternative to the extravagant (and problematic) infinities of eternal inflation (plus, no initial conditions problem) Predictions of observable levels of cosmic curvature from dSE cosmology will give an important future test

63. Albrecht Les Houches Lectures 2013 Pt. 463 Conclusions (Part 4) The search for a “big picture” of the Universe that explains why the region we observe should take this form has proven challenging, but has generated exciting ideas. We know we can do science with the Universe It appears that there is something right about cosmic inflation dSE cosmology offers a finite alternative to the extravagant (and problematic) infinities of eternal inflation (plus, no initial conditions problem) Predictions of observable levels of cosmic curvature from dSE cosmology will give an important future test (also, alternative to bubble start)

64. Les Houches Lectures on Cosmic Inflation Four Parts 1)Introductory material 2)Entropy, Tuning and Equilibrium in Cosmology 3)Classical and quantum probabilities in the multiverse 4)de Sitter equilibrium cosmology Andreas Albrecht; UC Davis Les Houches Lectures; July-Aug 2013 64Albrecht Les Houches Lectures 2013 Pt. 4 End Part 4

65. Albrecht Les Houches Lectures 2013 Pt. 465 Some parting thoughts We are *so* fortunate to be doing cosmology in these times Fantastic successes (slow roll inflation & structure) Great puzzles and challenges (the Guth dream, dark energy) Which ideas to import from everyday physics, which to throw out? Which ideas are too radical, which not radical enough? Let us all make the most of these amazing opportunities, and navigate these difficult issues as bravely and energetically as possible!