1. 1 Cosmic Inflation and the Arrow of Time A. Albrecht UCD P262 Spring 2006

2. 2 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

3. 3 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

4. 4 Inflation: Try and solve the following puzzles/features of the Standard Big Bang (SBB) universe: Flatness Homogeneity Monopole Horizon I.0 What is Cosmic Inflation?

5. 5 a  1 In the SBB, flatness is an “unstable fixed point”: At or The “GUT scale” Require to 55 decimal places to get today Dominates with time I.0 What is Cosmic Inflation? i

6. 6 Gravitational instability: The Jeans Length I.0 What is Cosmic Inflation? i Sound speed Average energy density Overdense regions of size collapse under their own weight. If the size is they just oscillate

7. 7 SBB Homogeneity: On very large scales the Universe is highly homogeneous, despite the fact that gravity will clump matter on scales greater than R Jeans At the GUT epoch the observed Universe consisted of 10 79 R Jeans sized regions.  The Universe was very smooth to start with. NB: Flatness & Homogeneity  SBB Universe starts in highly unstable state. i I.0 What is Cosmic Inflation?

8. 8 SBB Monopoles i I.0 What is Cosmic Inflation? A GUT phase transition (or any other process) that injects stable non-relativistic matter into the universe at early times (deep in radiation era, ie T i =10 16 GeV) will *ruin* cosmology: Monopole dominated Universe

9. 9 t=0 Here & Now SBB Horizon 10 80 causally disconnected regions at the GUT epoch i I.0 What is Cosmic Inflation? Horizon: The distance light has traveled since the big bang:

10. 10 I.0 What is Cosmic Inflation? The flatness, homogeneity & horizon features become “problems” if one feels one must explain initial conditions. Basically, the SBB says the universe must start in a highly balanced (or “fine tuned”) state, like a pencil on its point. Must/can one explain this? Inflation says “yes”

11. 11 The Basic Tools of Inflation: Consider a scalar field with: L If all space and time derivative (squared) terms Then Which implies Inflation w=-1 i I.0 What is Cosmic Inflation?

12. 12 A period of early inflation gives: Flatness: a  1 Dominates over & during inflation Homogeneity At horizon crossing: A suitably adjusted potential will give : i I.0 What is Cosmic Inflation? Evaluate when k=H during inflation

13. 13 A period of early inflation gives: Monopoles: a  1 Dominates over & during inflation (and ) i I.0 What is Cosmic Inflation? Monopoles are erased

14. 14 Inflation Horizon: Here & Now Inflation starts Inflation ends i I.0 What is Cosmic Inflation?

15. 15 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

16. 16 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

17. 17 I.1 Successes  Inflation: An early period of nearly exponential (“superluminal”) expansion set up the “initial” conditions for the standard big bang  Predictions:  total =1 (to one part in 100,000 as measured) Characteristic oscillations in the CMB power Nearly scale invariant perturbation spectrum Characteristic Gravity wave, CMB Polarization etc etc

18. 18  total=1 Bennett et al Feb 11 ‘03 WMAP I.1 Successes

19. 19  total=1 Bennett et al Feb 11 ‘03 WMAP I.1 Successes Tegmark et al astro-ph/0310723 WMAP Only WMAP + SDSS

20. 20 Characteristic oscillations in the CMB power Adapted from Bennett et al Feb 11 ‘03 WMAP “Active” models Inflation I.1 Successes Temperature Power   Angular scale

21. 21 Nearly scale invariant perturbation spectrum Bennett et al Feb 11 ‘03 WMAP I.1 Successes

22. 22 Characteristic Gravity wave, CMB Polarization etc Bennett et al Feb 11 ‘03 WMAP “Active” models Inflation TxE polarization power I.1 Successes

23. 23 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications Cosmic Inflation and the Arrow of Time

24. 24 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications Cosmic Inflation and the Arrow of Time

25. 25 Emerging prospects for high precisions tests |n S ’ | nsns n B. Gold & AA ‘03 I.2 Future tests Future Ly-alpha Generic slow roll inflation WMAP

26. 26 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

27. 27 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

28. 28 I.3 Theoretical advances A.A, Davis Meeting on Cosmic Inflation ‘03        

29. 29 I) Inflation in the era of WMAP  Great accomplishments and exiting future prospects For an “snapshot” view the slides at: inflation03.ucdavis.edu

30. 30 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

31. 31 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

32. 32 II.1 Introduction 1) The physical (“thermodynamic”) arrow of time 2) Cosmic Inflation Explained by initial conditions Explains the initial conditions of the cosmos Davies ’83 & ’84, Page ’83 (Nature) Q : How are these two related?

33. 33 Why wonder about arrow of time  inflation? Understand what we are really trying to accomplish with inflation  more solid foundations Fun combination of physics ideas Evaluate “alternatives to inflation” II.1 Introduction Window on current hot topics

34. 34 Initial conditions in ”normal Physics”: - Pose physical question - Chose initial conditions which best describe “apparatus” - Calculate and compare with experimental results Cosmic Inflation: Explain cosmic initial conditions using physics Initial conditions play supporting role Laws of physics play supporting role Examples: - Arrow of time - Choice of vacuum in quantum field theory II.1 Introduction

35. 35 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

36. 36 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

37. 37 See H.D. Zeh The physical basis of the direction of time - Macroscopic (or thermodynamic) arrow of time emerges from a combination of: Dynamical trends or “attractors” Special initial conditions Choice of coarse graining - Despite a completely reversible microscopic world II.2 Arrow of time basics NB: Not about “T symmetry”

38. 38, gravity unimportant)(Taking Dynamical trends or “attractors”  Special initial conditions  Choice of coarse graining  An Example: II.2 Arrow of time basics

39. 39 Recording/Learning Harnessing energy (actually “low entropy”) Key roles of the arrow of time: II.2 Arrow of time basics

40. 40 Key roles of the arrow of time (cont.): Quantum Measurement Everett  same old “thermodynamic” arrow of time II.2 Arrow of time basics

41. 41 - Macroscopic (or thermodynamic) arrow of time emerges from a combination of: Dynamical trends or “attractors” Special initial conditions Choice of coarse graining Most Fundamental Entropy, laws of thermodynamics, counting number of states etc: -Ways to quantify the above - “Icing on the cake” II.2 Arrow of time basics

42. 42 Time 1 Time 2Time 3 II.2 Arrow of time basics

43. 43 : gravity very importantNow consider A completely different trend/attractor: Gravitational Collapse II.2 Arrow of time basics

44. 44 : gravity very important Equilibrium under gravitational collapse: Black Hole (the state of ultimate collapse) (S bh not as well developed as ordinary entropy, but good enough for our purposes as a way to quantify a dynamical trend.) II.2 Arrow of time basics

45. 45 The Punch Line: The thermodynamic arrow of time originates with the very special initial conditions of the cosmos: The early universe is very homogeneous on scales  very far from Eqm. (= black hole) Cosmic Microwave Background uniform to one part in 10 5 Penrose II.2 Arrow of time basics

46. 46 The everyday link to gravitational collapse II.2 Arrow of time basics

47. 47 The everyday link to gravitational collapse II.2 Arrow of time basics

48. 48 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

49. 49 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

50. 50 II.3 Inflation and the arrow of time Standard inflation spiel begins: Cosmological problems of standard big bang: Universe starts far from dynamical trend: -Flat -Homogeneous -Horizons prevent dynamical explanation Q: How can this fact be explained? But isn’t starting far from the dynamical trend exactly what is required to explain the arrow of time? And when do we ever explain initial conditions anyway?

51. 51 Warm up 1: Big Bang Nucleosynthesis Prediction of abundances. Time  Mass Fraction  Species But doesn’t the answer just depend on the initial state? Figure: Burles, Nollett, &Turner II.3 Inflation and the arrow of time

52. 52 Warm up 1: Big Bang Nucleosynthesis: Nuclear Statistical (“chemical”) equilibrium (attractor) erases initial conditions dependence. Time  Mass Fraction  Eq. Time Time to species freeze-out Coarse Graining: Just ask about mass fractions II.3 Inflation and the arrow of time

53. 53 Warm up 2: Gas in ice Ice Insulator Ice Time 1 Insulator II.3 Inflation and the arrow of time

54. 54 Ice Insulator Ice Time 2 Insulator Warm up 2: Gas in ice II.3 Inflation and the arrow of time

55. 55 Ice Insulator Ice Time 3 Insulator Frozen Warm up 2: Gas in ice II.3 Inflation and the arrow of time

56. 56 Internal eqm time << freezing time  Internal eqm. set initial conditions for condensation & final frozen state. Warm up 2: Gas in ice II.3 Inflation and the arrow of time

57. 57 End warm up… now the real thing: II.3 Inflation and the arrow of time

58. 58 Key ingredient: Cosmological constant => different gravitational at attractor: de Sitter space - Perfectly flat, homogeneous, exponentially expanding Properties of Big Bang initial state Gibbons & Hawking, See also Bousso Equivalent to “perfect” potential dominated state II.3 Inflation and the arrow of time

59. 59 Can be mimicked by a scalar field in a special “potential dominated state” Inflaton field can turn on and off Inflation: Let the inflaton field turn on and leave it on for *many* de Sitter equilibration times, then decay into ordinary matter. A standard “big bang” (arrow of time and all) is created. II.3 Inflation and the arrow of time

60. 60 The Inflaton: Consider a scalar field with: L If all space and time derivative (squared) terms Inflation V Quantum fluctuations II.3 Inflation and the arrow of time

61. 61 Comparisons: SystemInitial Conditions Nucleosynthesis Slow Freeze Inflation V Created by early time attractor (eqm) II.3 Inflation and the arrow of time

62. 62 Comparisons: SystemInitial Conditions Nucleosynthesis Slow Freeze Inflation V Created by early time attractor (eqm) in subspace But driven by non- eqm degree of freedom Background Spacetime Out of eqm ice Special Inflaton field configuration Issues with very small scales! II.3 Inflation and the arrow of time

63. 63 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

64. 64 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

65. 65 Does inflation -Predict the arrow of time? (Sets up IC’s for Big Bang) -Depend on the arrow of time? (Requires special initial state of inflaton etc.) II.4 Implications

66. 66 LAB Comment on how we use knowledge (“A” word!) Total knowledge about the universe  InputTheoryOutput II.4 Implications

67. 67 LAB Comment on the “A” word: Total knowledge about the universe  InputTheoryOutput II.4 Implications

68. 68 LAB Comment on the “A” word: Total knowledge about the universe  InputTheoryOutput II.4 Implications

69. 69 LAB Comment on the “A” word: Total knowledge about the universe  InputTheoryOutput II.4 Implications

70. 70 LAB Comment on the “A” word: Total knowledge about the universe  InputTheoryOutput LAB PRED II.4 Implications

71. 71 LAB InputTheoryOutput LAB PRED The best science will use up less here and produce more here II.4 Implications

72. 72 Q: To what extent should our arrow of time (smooth initial state of Big Bang) best used as INPUT, rather than OUTPUT? A: The arrow of time (smooth initial state of Big Bang) can NOT be 100% output. The very nature of the arrow of time requires initial conditions that are not completely generic II.4 Implications

73. 73 What Role  What role inflation? -Gives package deal: Universe very large, flat, and with particular perturbations (falsifiable!). -Answers Boltzmann’s concerns about typical regions with arrow of time being much smaller and “shorter” then we experience. (inflation as amplifier). [Also modern cosmological version.] - Answers “How did our Universe come about?” II.4 Implications NB: In the spirit of Linde’s “chaotic inflation” -“Dominant channel” into Big Bang (Uses attractor behavior and exponential volume factors to maximize impact)

74. 74 Rare Fluctuation II.4 Implications

75. 75 II.4 Implications Boltzmann's “cosmology”:

76. 76 II.4 Implications Boltzmann's “cosmology”:

77. 77 II.4 Implications Boltzmann's “cosmology”:

78. 78 II.4 Implications Boltzmann's “cosmology”:

79. 79 II.4 Implications Boltzmann's “cosmology”:

80. 80 II.4 Implications Boltzmann's “cosmology”:

81. 81 II.4 Implications Boltzmann's “cosmology”:

82. 82 II.4 Implications Boltzmann's “cosmology”:

83. 83 II.4 Implications Boltzmann's “cosmology” appeared to make very strange predictions:

84. 84 II.4 Implications Boltzmann's “cosmology”:

85. 85 II.4 Implications Boltzmann's “cosmology”:

86. 86 II.4 Implications Boltzmann's “cosmology”: (Boltzmann's brain)

87. 87 II.4 Implications Boltzmann's “cosmology”:

88. 88 II.4 Implications Boltzmann's “cosmology”:

89. 89 II.4 Implications Boltzmann's “cosmology”:

90. 90 II.4 Implications Inflation (**schematic**):

91. 91 II.4 Implications Inflation (**schematic**):

92. 92 II.4 Implications all space and time derivative (squared) terms V Inflation (**schematic**): The “rare fluctuation” is in the inflaton field

93. 93 II.4 Implications Inflation exponentially expands the volume Reheated regions give big bang Special package of features predicted by inflation Inflation (**schematic**):

94. 94 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

95. 95 I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes I.2 Future tests I.3 Theoretical advances III) Conclusions II) Inflation and the arrow of time II.1 Introduction II.2 Arrow of time basics II.3 Inflation and the arrow of time II.4 Implications II.5 Can the Universe Afford Inflation? Cosmic Inflation and the Arrow of Time

96. 96 Dark energy and Equilibrium

97. 97 Supernova Preferred by modern data  Amount of gravitating matter   Amount of “antigravity” matter  (Dark Energy) Red line: No anti-gravity matter Mass-Energy of the a Universe made only out of standard model matter Surprise factor II.5 Can the Universe afford Inflation?

98. 98 An interesting property of some types of dark energy (including a w=-1 cosmological constant): Formation of an event horizon: Black Hole Event Horizon (schematic): Outside observer sees in-falling object take infinite time to reach the horizon (“never reaches the horizon”) II.5 Can the Universe afford Inflation?

99. 99 An interesting property of some types of dark energy (including the cosmological constant): Formation of an event horizon: Dark Energy Event Horizon (schematic): INSIDE observer sees OUT-flying object take infinite time to reach the horizon (“never reaches the horizon”) t1t2t3t4…… “de Sitter Space” II.5 Can the Universe afford Inflation?

100. 100 “De Sitter Space: The ultimate equilibrium for the universe? Horizon Quantum effects: Hawking Temperature II.5 Can the Universe afford Inflation?

101. 101 Rare Fluctuation A cosmological constant can help realize the “rare fluctuation” cosmology. II.5 Can the Universe afford Inflation?

102. 102 Rare Fluctuation A cosmological constant can help realize the “rare fluctuation” cosmology. II.5 Can the Universe afford Inflation? The only really physics way to discuss “initial” conditions

103. 103 Concept: Realization: “de Sitter Space” II.5 Can the Universe afford Inflation?

104. 104 Rare Fluctuation II.5 Can the Universe afford Inflation?

105. 105 Big question: What is the most likely fluctuation to “give what we see:?: -Normal Big Bang? -Inflating Region? II.5 Can the Universe afford Inflation?

106. 106  The universe spends most of its time in “equilibrium”  The equilibrium state is given by an observer’s “causal patch” in de Sitter space with a very small Λ.  Cosmology given by the appearance of rare fluctuations away from this eqm. state.  Recurrence times/probabilities given by stat mech: Dyson, Kleban & Susskind (hep-th/0208013) AND AA & Sorbo hep-th/0405270 The basic picture: II.5 Can the Universe afford Inflation?

107. 107 = Recurrence time for a particular fluctuation = Recurrence time for whole system = Total microstates of system = Probability of fluctuation II.5 Can the Universe afford Inflation?

108. 108 A&S: How to calculate the inflationary fluctuation the Darwinian cosmology with Λ : 1) Use standard work on tunneling into inflation (“free lunch”, “universe in a garage”) Farhi Guth & Gueven; Blau Gundelman & Guth; Fischler Morgan & Polchinski 2) Use stat mech to determine Pc for the classical solutions in 1) quantum tunneling Probability to form “incoming” classical solution AA & Sorbo hep-th/0405270 II.5 Can the Universe afford Inflation?

109. 109 Picture from A. Guth II.5 Can the Universe afford Inflation?

110. 110 The stat mech piece for de Sitter space with a small perturbation looks Schwarzschild far from the perturbation: Gibbons & Hawking II.5 Can the Universe afford Inflation?

111. 111 The stat mech piece for de Sitter space with a small perturbation looks Schwarzschild far from the perturbation: Gibbons & Hawking So where Dominated by reduction in entropy of full system (not S I ) II.5 Can the Universe afford Inflation?

112. 112 Box of gas analogy Rare fluctuation in a box of gas: fraction of V affected size of fluctuation as a fraction of fV Assuming entropy density (s) obeys and using conservation of energy Entropy of remaining “normal” region Entropy of “weird” region The dominant effect is that a volume fV has been deprived of eqm entropy II.5 Can the Universe afford Inflation?

113. 113 The Answer: II.5 Can the Universe afford Inflation?

114. 114 The Answer: and II.5 Can the Universe afford Inflation?

115. 115 The Answer: and Dominated by “entropy lost by environment” II.5 Can the Universe afford Inflation?

116. 116 Compare with “regular big bang” II.5 Can the Universe afford Inflation?

117. 117 Compare with “regular big bang” so Inflation highly favored II.5 Can the Universe afford Inflation?

118. 118 Inflation highly favored This is a quantification of the standard intuition: Inflation starts with a “cheap” fluctuation vs Standard Big Bang This makes a inflation “more likely” start for our observed universe. II.5 Can the Universe afford Inflation?

119. 119 BUT

120. 120 Outside observer sees in-falling object take infinite time to reach the horizon (“never reaches the horizon”) iii. Horizons, Entropy and Causal Patch Physics Black Hole Event Horizon (schematic): II.5 Can the Universe afford Inflation?

121. 121 Outside observer sees in-falling object take infinite time to reach the horizon (“never reaches the horizon”) Black Hole Event Horizon (schematic): Principles of Causal Patch Physics: To the outside observer there is no “inside of Black Hole” Infalling observer reuses the same degrees of freedom to describe the interior* (outside observer absent) Could resolve BH info paradox iii. Horizons, Entropy and Causal Patch Physics *Requires highly non-local transformation between frames (“stringy magic”?) II.5 Can the Universe afford Inflation?

122. 122 Implications of causal patch physics for our calculations: Basis for De Sitter space as finite closed system & application of stat mech During inflation (quasi-De Sitter) a horizon forms: Possibly dramatic implications. Dyson Kleban & Susskind: There is no “outside the De Sitter horizon” during inflation. All degrees of freedom are inside. II.5 Can the Universe afford Inflation?

123. 123 Principles of causal patch physics change everything: DKS: A horizon forms for the inflating region and holographic magic is evoked: de Sitter + small fluctuation (mass M) “Magic” Inflation: approximate de Sitter  degrees of freedom re- organize to only describe inside the horizon.  Most degrees of freedom must “condense out” to manifest the very low inflationary entropy. II.5 Can the Universe afford Inflation?

124. 124 Principles of causal patch physics change everything: DKS: A horizon forms for the inflating region and holographic magic is evoked: de Sitter + small fluctuation (mass M) “Magic” Inflation: approximate de Sitter  degrees of freedom re- organize to only describe inside the horizon.  Most degrees of freedom must “condense out” to manifest the very low inflationary entropy.

125. 125 Causal patch principles replace with Inflation highly disfavored Inflation highly favored II.5 Can the Universe afford Inflation?

126. 126 Causal patch principles replace Inflation highly favored with Low entropy of inflating region converted from benefit to liability Inflation highly disfavored Counting of exterior makes inflation cheap II.5 Can the Universe afford Inflation?

127. 127 v. Discussion & Conclusions Topics Transcending the specifics of de Sitter eqm Boltzmann’s Brain Conclusions II.5 Can the Universe afford Inflation?

128. 128 Transcending the specifics of de Sitter eqm This looks like a problem no matter how confused you are about what to put here II.5 Can the Universe afford Inflation?

129. 129 This is rare no matter how poorly you understand the entropy at Time 1 Time 1 Time 2 II.5 Can the Universe afford Inflation?

130. 130 And this is even more rare! Time 1 Time 2 II.5 Can the Universe afford Inflation?

131. 131 Surely this is rare too landscape II.5 Can the Universe afford Inflation?

132. 132 and this! Eternal inflation II.5 Can the Universe afford Inflation?

133. 133 Landscapes and eternal inflation etc do not obviously get you off the hook. For example for large spaces, consider the limit This looks like a problem no matter how confused you are about what to put here II.5 Can the Universe afford Inflation?

134. 134 Boltzmann’s Brain paradox:  The most likely fluctuation consistent with everything you know is your brain fluctuating out of chaos and immediately re-equilibrating. (Also works for planets) [Related to in DKS]  Only inflation has an answer to this paradox. With inflation, most probable way to create one brain (or planet) comes packaged with a huge flat universe (+body, fellow creatures etc)  This is as least as important as the other successes of inflation!

135. 135 Conclusions  Darwinian cosmology is better  DKS /AS/ Λ offer an attractive scheme for Darwinian cosmology. Can bring discussions of inflation/etc to next level.  Cosmology appears to place causal patch physics in conflict with inflation (even when not using Λ eqm. ).  Fundamental issue: Is there really more universe outside the horizon during inflation? (yes  inflation OK)  Resolving this conflict between will teach us something very interesting about at least one of these: -inflation -causal patch physics -quantum gravity II.5 Can the Universe afford Inflation?

136. 136 END

137. 137 Burning question: What is the most likely fluctuation to “give what we see:?: -Normal Big Bang? -Inflating Region?

138. 138 Additional material

139. 139 Where to go from here: How to fit all this into a “big picture” - Can inflation be “eternal”? (Brode, Vilenkin, Guth, Aguirre & Gratton) - Connection with quantum gravity, quantum measurement… (Banks, Banks & Fischler, Dyson et al, AA Kaloper & Song) - Quantify “dominant channel” claim - etc. Evaluate competing ideas: - Ekpyrotic (no “attractor”, no volume factors. How can this channel compete?... a super-rare fluctuation) - Cyclic (“a perpetual motion machine of the 2 nd kind”?) - Holographic (built in arrow of time) II.4 Implications

140. 140  More thoughts Q: Can the thermodynamic arrow of time be sufficiently tightly linked with emergence of classicality to reduce waste of data as input? (Do classical “regions” automatically have a “low S end”?) Related to standard “wavefunction of the universe” work II.4 Implications Does gravity radically transform the nature of the arrow of time?

141. 141  More thoughts: -Sort our measures! (Usually we can handle this.) - How can we contemplate the “general chaotic state of all possibilities”? vs eternal inflation, vs causal patch physics II.4 Implications

142. 142  Evaluate alternatives Attractor behavior vs “statement of state” (i.e ekpyrotic) Special initial conditions must be somewhere (vs. early statements about the “new” cyclic universe) II.4 Implications

143. 143 Idea “Creates” IC’s (attractor behavior) Volume Factors Standard Big Bang no Holographic Cosmology (Banks & Fischler)** Inflation (Chaotic = ++) Wavefunction of Univ. ? VSL Cosmology Ekpyrotic Universeno Eternal (Aguirre & Gratton) New Cyclic II.4 Implications no yes yes (w/inflation) yes“Yes” no Version 1 Version 2 noX yes noX

144. 144 III Conclusions I) Inflation in the era of WMAP I.1 Successes I.2 Future tests I.3 Theoretical advances  Exciting future

145. 145 Why wonder about arrow of time  inflation? Understand what we are really trying to accomplish with inflation  a more solid foundation Inflation: 1) Can not take all possible initial conditions into SBB 2) Can give “dominant channel” to Standard Big Bang.. (Still have predictive power, successful so far) 3) Solves the “Boltzmann’s Brain” problem III Conclusions II) Inflation and the arrow of time -Initial attractor -Volume factor Special inflaton initial state (arrow of time) Required of all theories

146. 146 Why wonder about arrow of time  inflation? Evaluate “alternatives to inflation” 1)Attractor behavior is not the same as “statement of state” 2)Arrow of time  all theories of initial conditions require something “special” (not completely generic) 3)(No Perpetual Motion!) III Conclusions II) Inflation and the arrow of time “Statement of state” much less ambitious

147. 147 Why wonder about arrow of time  inflation? III Conclusions II) Inflation and the arrow of time Window on current hot topics 1)Singularities in quantum gravity 2)“Equilibrium” states in quantum gravity 3)Entropy and gravity (“Holography”) (AA, NK, Y- SS) 4)“Before” inflation 5)Arrow of time in quantum gravity

148. 148 Why wonder about arrow of time  inflation? Fun combination of physics ideas III Conclusions II) Inflation and the arrow of time