Cosmic Inflation Tutorial - PDF Free Download

Cosmic Inflation Tutorial Andreas Albrecht Center for Quantum Mathematics and Physics (QMAP) and Department of Physics UC Davis Simons Workshop on Quantum Information in Cosmology Niels Bohr Institute April 2018 A. Albrecht Inflation Tutorial NBI 2018 1

Cosmic Inflation: Concrete technical idea with great phenomenology Couched in the language of solving tuning problems Big open questions A. Albrecht Inflation Tutorial NBI 2018 2

Cosmic Inflation: Concrete technical idea with great phenomenology Couched in the language of solving tuning problems Big open questions A. Albrecht Inflation Tutorial NBI 2018 3

Conclusions A) Inflation is a technical tool for connecting cosmological observables with high energy physics. Impressive successes. B) However, without a meta theory about how inflation started (and how it competes with other scenarios, such as the Standard Big Bang) big questions are unresolved. C) Complex sociology as different individuals choose to give A) and B) different weight. A. Albrecht Inflation Tutorial NBI 2018 4

Cosmic Inflation: Concrete technical idea with great phenomenology Couched in the language of solving tuning problems Big open questions A. Albrecht Inflation Tutorial NBI 2018 7

Cosmic Inflation: Concrete technical idea with great phenomenology Couched in the language of solving tuning problems Big open questions A. Albrecht Inflation Tutorial NBI 2018 8

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 9

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 10

Einstein equation + Homogeneity & Isotropy Friedmann Eqn. H 2 2 a 8 = = G + + + a 3 ( ) k r m DE A. Albrecht Inflation Tutorial NBI 2018 11

Friedmann Eqn. H 2 2 a 8 = = G + + + a 3 ( ) k r m DE A. Albrecht Inflation Tutorial NBI 2018 12

Friedmann Eqn. H 2 2 a 8 = = G + + + a 3 ( ) k r m DE Hubble parameter ( constant, because today it takes ~10Billion years to change appreciably) A. Albrecht Inflation Tutorial NBI 2018 13

Friedmann Eqn. H 2 2 a 8 = = G + + + a 3 ( ) k r m DE Hubble parameter ( constant, because today it takes ~10Billion years to change appreciably) Scale factor A. Albrecht Inflation Tutorial NBI 2018 14

Friedmann Eqn. a 2 H 2 2 a 8 = = G + + + a 3 ( ) k r m DE Curvature Scale factor A. Albrecht Inflation Tutorial NBI 2018 15

Friedmann Eqn. a 2 a 4 H 2 2 a 8 = = G + + + a 3 ( ) k r m DE Curvature Relativistic Matter Scale factor A. Albrecht Inflation Tutorial NBI 2018 16

Friedmann Eqn. a 2 a 4 a 3 H 2 2 a 8 = = G + + + a 3 ( ) k r m DE Curvature Relativistic Matter Non-relativistic Matter Scale factor A. Albrecht Inflation Tutorial NBI 2018 17

Friedmann Eqn. a 2 a 4 0 a a 3 H 2 2 a 8 = = G + + + a 3 Curvature ( ) Relativistic Matter k r m DE Non-relativistic Matter Dark Energy Scale factor A. Albrecht Inflation Tutorial NBI 2018 18

log(/ c 0 ) Evolution of Cosmic Matter 120 100 80 r m 60 40 20 0-20 -30-20 -10 0 10 log(a/a 0 ) Today A. Albrecht Inflation Tutorial NBI 2018 19

Time The History of the Universe Today Dark Energy Galaxy Formation Last Scattering Nuclear & HEP High Energy & Temp Inflation? Extra Dimensions? A. Albrecht Inflation Tutorial NBI 2018 20

Time The History of the Universe Image of the Last Scattering Surface or edge of opaqueness High Energy & Temp A. Albrecht Inflation Tutorial NBI 2018 21

Time The History of the Universe Image of the Last Scattering Surface or edge of opaqueness High Energy & Temp A. Albrecht Inflation Tutorial NBI 2018 22

log(/ c 0 ) 120 100 80 The curvature feature/ problem k r m 60 40 20 0-20 -30-20 -10 0 10 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 23

log(/ c 0 ) 120 100 80 The curvature feature/ problem k r m 60 40 20! 0-20 -30-20 -10 0 10 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 24

log(/ c 0 ) The curvature feature/ problem 120 100 80 60 40 k r m 20 0! -20-30 -20-10 0 10 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 25

log(/ c 0 ) The curvature feature/ problem 120 100 80 r m 60 40 k 20 0! -20-30 -20-10 0 10 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 26

log(/ c 0 ) The curvature feature/ problem 120 100 80 60 40 20 0 r m k -20-30 -20-10 0 10 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 27

log(/ c 0 ) 120 100 80 60 40 20 0 The curvature feature/ problem! r m k -20-30 -20-10 0 10 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 28

In the SBB, flatness is an unstable fixed point : i 1 W a W 2 a 2 8 H = a c c 3 3H 8 2 k a 2 or At T a a 0 16 =10 = 10 GeV 28 The GUT scale a 3, a 4 Dominates with time Require = c to 55 decimal places to get c today I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 29

In the SBB, flatness is an unstable fixed point : i 1 W a W 2 a 2 8 H = a SBB = Standard Big Bang cosmology, or cosmology without c inflation. c 3 3H 8 2 k a 2 or At T a a 0 16 =10 = 10 GeV 28 The GUT scale a 3, a 4 Dominates with time Require = c to 55 decimal places to get c today I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 30

i Gravitational instability: The Jeans Length R I.0 What is Cosmic Inflation? 2 c c G Jeans J s Sound speed Overdense regions of size collapse under their own weight. If the size is oscillate R Jeans they just R Jeans 1/ 2 A. Albrecht Inflation Tutorial NBI 2018 Average energy density 31

SBB Homogeneity: i 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. S 10 S = 10 4 M 35 35 2 Univ bh Max Univ I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 32

log(/ c 0 ) 120 100 80 The monopole problem Mono r m 60 40 20 0-20 -30-20 -10 0 10 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 33

log(/ c 0 ) 120 100 80 The monopole problem Mono r m 60 40 20 0! -20-30 -20-10 0 10 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 34

i SBB Monopoles 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: M Normal T 3 T M( Ti) Ti M( Ti) Ti = = " " 4 T Normal ( Ti ) T Normal ( Ti ) Ti Monopole dominated Universe I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 35

i SBB Horizon t=0 10 80 causally disconnected regions at the GUT epoch d H Horizon: The distance light has traveled since the big bang: Here & Now dt ' dh = a( t) dt ' at ( ') t 0 I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 36

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 I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 37

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 38

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 39

Friedmann Eqn. a 2 a 4 0 a a 3 H 2 2 a 8 = = G + + + a 3 Curvature ( ) Relativistic Matter k r m DE Non-relativistic Matter Dark Energy A. Albrecht Inflation Tutorial NBI 2018 40

Now add cosmic inflation Friedmann Eqn. a 0 a 2 a 4 0 a a 3 H 2 2 a 8 = = G + + + + a 3 Inflaton Curvature ( ) I k r m DE Relativistic Matter Non-relativistic Matter Dark Energy A. Albrecht Inflation Tutorial NBI 2018 41

Now add cosmic inflation Friedmann Eqn. a 0 a 2 a 4 0 a a 3 H I H a = const a 2 2 a 8 = = G + + + + a 3 Inflaton Curvature a e Ht ( ) I k r m DE Relativistic Matter Non-relativistic Matter Dark Energy A. Albrecht Inflation Tutorial NBI 2018 42

Now add cosmic inflation Friedmann Eqn. a 0 H 2 2 a 8 = = G + + + + a 3 Inflaton Curvature ( ) I k r m DE Relativistic Matter Non-relativistic Matter Dark Energy A. Albrecht Inflation Tutorial NBI 2018 43

The inflaton: ~Homogeneous scalar field obeying + 3H = V ( ) Cosmic damping Coupling to ordinary matter All potentials have a low roll (overdamped) regime where 1 I = + V ( ) V ( ) const. a 2 2 0 V A. Albrecht Inflation Tutorial NBI 2018 45

log(/ c 0 ) Add a period of Inflation: 120 100 80 60 40 20 0 I r m -20-60 -40-20 0 20 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 47

log(/ c 0 ) With inflation, initially large curvature is OK: 120 100 I r 80 m 60 k 40 20 0-20 -60-40 -20 0 20 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 48

log(/ c 0 ) With inflation, early production of large amounts of non-relativistic matter (monopoles) is ok : 120 100 I r 80 m 60 Mono 40 20 0-20 -60-40 -20 0 20 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 49

Inflation detail: log(/ c 0 ) 110 105 KE V r 100-28.8-28.6-28.4-28.2-28 -27.8-27.6 0.5 /M P 0-0.5-28.8-28.6-28.4-28.2-28 -27.8-27.6 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 51

log(/ c 0 ) Inflation detail: 110 105 KE V 4 V/M GUT 3 2 1 V 1 2 2 2 ( ) = m 100 0-28.8-28.6-28.4-28.2-28 -2-27.8-27.6 0 2 /M P 0.5 r /M P 0-0.5-28.8-28.6-28.4-28.2-28 -27.8-27.6 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 52

Hubble Length 2 2 a 8 8 H = = G ( + + + + ) G a 3 3 I k r m DE Tot R H c H 1 1/2 Tot A. Albrecht Inflation Tutorial NBI 2018 53

log(r H /R H 0 ) 10 0-10 R H c 1 H Tot 1/2 R H -20-30 -40-50 -60-60 -40-20 0 20 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 54

log(r H /R H 0 ) 10 0-10 -20-30 -40-50 R i H c 1 Hi i 1/2 I R H r R H m R H R H -60-60 -40-20 0 20 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 55

log(r H /R H 0 ) 10 0-10 -20-30 -40-50 R i H c 1 Hi i 1/2 I R H r R H m R H R H Tot R H -60-60 -40-20 0 20 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 56

log(r H /R H 0 ) 10 0-10 R H c 1 H Tot 1/2 R H -20-30 -40-50 -60-60 -40-20 0 20 log(a/a 0 ) A. Albrecht Inflation Tutorial NBI 2018 57

log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length 10 0-10 -20-30 -40-50 -60 End of inflation -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 58

log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length 10 0-10 -20-30 -40-50 -60 End of reheating -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 59

log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length 10 0-10 -20-30 -40-50 -60 Weak Scale -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 60

log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length 10 0-10 -20-30 -40-50 -60 BBN -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 61

log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length 10 0-10 -20-30 -40-50 -60 Radiation- Matter equality -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 62

log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length 10 0-10 Today -20-30 -40-50 -60-70 -60-50 -40-30 -20-10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 63

log(r H /R H 0 ) Perturbations from inflation 10 0-10 -20-30 -40-50 -60-70 -60-50 -40-30 -20-10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 64

log(r H /R H 0 ) Perturbations from inflation 10 0-10 Here -20-30 -40-50 -60-70 -60-50 -40-30 -20-10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 65

log(r H /R H 0 ) Perturbations from inflation 10 0-10 -20 2 H Here Here -30-40 -50-60 -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 66

log(r H /R H 0 ) 10 0-10 -20 2 H Here Here -30-40 -50-60 -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 67

log(r H /R H 0 ) 10 0-10 -20 2 H Here Here -30-40 -50-60 -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 68

log(r H /R H 0 ) 10 0-10 -20 2 H Here Here -30-40 -50-60 Short wavelength QFT modes taken to be in vacuum state (the Bunch Davies -70 Vacuum ) -60-50 -40-30 -20-10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 69

log(/ c 0 ) Inflation detail: 110 105 KE V 4 V/M GUT 3 2 1 V 1 2 2 2 ( ) = m 100 0-28.8-28.6-28.4-28.2-28 -2-27.8-27.6 0 2 /M P 0.5 r /M P 0 m = 810 to give -0.5-28.8-28.6-28.4-28.2-28 -27.8 5-27.6 10 log(a/a 0 ) 12 GeV A. Albrecht Inflation Tutorial NBI 2018 71

log(r H /R H 0 ) 10 0-10 -20 2 H Here Here -30-40 -50-60 -70-60 -50-40 -30-20 -10 0 10 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 73

arxiv:1210.7231v1 A. Albrecht Inflation Tutorial NBI 2018 74

Planck CMB data Inflation theory A. Albrecht Inflation Tutorial NBI 2018 75

The Basic Tools of Inflation: i Consider a scalar field with: 1 L ( ) = V ( ) 2 If V( ) all space and time derivative (squared) terms Then T V ( ) 0 0 0 0 V ( ) 0 0 0 0 V ( ) 0 0 0 0 V ( ) d da Which implies p = 0 w=-1 a~ e Ht Inflation I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 76

A period of early inflation gives: i Flatness: 2 a 2 8 k H = 2 a 3 a 1 a = const. Dominates over during inflation r & m W W c 1 Homogeneity At horizon crossing: Evaluate when k=h during inflation 2 H HV ' 2 H 2 A suitably adjusted potential will give : H H 10 5 const I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 77

A period of early inflation gives: i Monopoles: 2 a 2 8 H = a 3 k a 2 1 W W c 1 a r Dominates over & during inflation (and ) M m M a ( a ) a 3 1 M 1 a M ( a1 ) = = ( a) = Const ( a 1 ) e a 3Ht Monopoles are erased ~ Ht e 0 I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 78

i Inflation Horizon: Inflation starts Inflation ends Here & Now I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI 2018 79

I) Inflation in the era of WMAP I.0 What is Cosmic Inflation? I.1 Successes 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? III) Conclusions A. Albrecht Inflation Tutorial NBI 2018 Cosmic Inflation and the Arrow of Time 80

Inflation: An early period of nearly exponential expansion set up the initial conditions for the standard big bang Predictions: W 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 I.1 Successes A. Albrecht Inflation Tutorial NBI 2018 81

Wtotal=1 WMAP Bennett et al Feb 11 03 A. Albrecht Inflation Tutorial NBI 2018 82

Temperature Power Characteristic oscillations in the CMB power WMAP Inflation Active models Angular scale Adapted from Bennett et al Feb 11 03 A. Albrecht Inflation Tutorial NBI 2018 83

Nearly scale invariant perturbation spectrum WMAP k ( ) H= k = Ak 1 ns Bennett et al Feb 11 03 A. Albrecht Inflation Tutorial NBI 2018 84

Characteristic Gravity wave, CMB Polarization etc WMAP TxE polarization power Inflation Active models Bennett et al Feb 11 03 A. Albrecht Inflation Tutorial NBI 2018 85

https://www.aanda.org/articles/aa/full_html/2016/10/aa25898-15/aa25898-15.html fig 55 A. Albrecht Inflation Tutorial NBI 2018 86

What happened before inflation? A. Albrecht Inflation Tutorial NBI 2018 87

What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation A. Albrecht Inflation Tutorial NBI 2018 88

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 89

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 90

Eternal inflation A. Albrecht Inflation Tutorial NBI 2018 91

Quantum fluctuations during slow roll: R H A region of one field coherence length ( = R H ) gets a new quantum contribution to the field value from an uncorrelated commoving mode of size = H 1 in a time t = H leading to a (random) quantum rate of change: 2 Q = H t Thus 2 Q H = measures the importance of quantum fluctuations in the field evolution A. Albrecht Inflation Tutorial NBI 2018 92

Quantum fluctuations during slow roll: R H A region of one field coherence length ( = R H ) gets a new quantum contribution to the field value from an uncorrelated commoving mode of size = H 1 in a time t = H leading to a (random) quantum rate of change: 2 Q = H t Thus 2 Q H 10 5 = ( ) measures the importance of quantum fluctuations in the field evolution A. Albrecht Inflation Tutorial NBI 2018 93

Quantum fluctuations during slow roll: R H For realistic perturbations the evolution is very classical A region of one field coherence length ( = R H ) gets a new quantum contribution to the field value from an uncorrelated commoving mode of size = H 1 in a time t = H leading to a (random) quantum rate of change: 2 Q = H t Thus 2 Q H = 10 5 = ( ) measures the importance of quantum fluctuations in the field evolution A. Albrecht Inflation Tutorial NBI 2018 94

Quantum fluctuations during slow roll: R H For realistic perturbations the evolution is very classical (But not as classical as most classical things we know!) A region of one field coherence length ( = R H ) gets a new quantum contribution to the field value from an uncorrelated commoving mode of size = H 1 in a time t = H leading to a (random) quantum rate of change: 2 Q = H t Thus 2 Q H = 10 5 = ( ) measures the importance of quantum fluctuations in the field evolution A. Albrecht Inflation Tutorial NBI 2018 95

4 2.5 2 V/M GUT 1.5 1 0.5 If this region produced our observable universe 0-2 -1 0 1 2 /M P A. Albrecht Inflation Tutorial NBI 2018 96

4 2.5 2 V/M GUT 1.5 1 0.5 If this region produced our observable universe 0-2 -1 0 1 2 /M P A. Albrecht Inflation Tutorial NBI 2018 97

2.5 V/M GUT 4 2 1.5 1 It seems reasonable to assume the field was rolling up here beforehand (classical extrapolation) 0.5 0-2 -1 0 1 2 /M P A. Albrecht Inflation Tutorial NBI 2018 98

log[(r H /R H 0 )] Evolution of Cosmic Length 10 0-10 -20-30 -40-50 -60-70 -80-60 -50-40 -30-20 -10 0 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 99

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 150 100 50 10 4 0-50 -100-150 -200-150 -100-50 0 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 100

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 600 400 200 0 10 4-200 -400-600 -600-500 -400-300 -200-100 0 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 101

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 2000 1500 1000 10 3 500 0-500 -1000 10 4-1500 -2000-1500 -1000-500 0 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 102

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 6000 4000 2000 0-2000 10 3-4000 -6000-6000 -5000-4000 -3000-2000 -1000 0 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 103

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) x 10 4 2 1.5 1 10 2 0.5 0-0.5-1 -1.5-2 10 3-15000 -10000-5000 0 log(a/a ) 0 A. Albrecht Inflation Tutorial NBI 2018 104

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 6 x 10 4 4 2 0-2 10 2-4 -6-6 -5-4 -3-2 -1 0 log(a/a ) 0 x 10 4 A. Albrecht Inflation Tutorial NBI 2018 105

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) x 10 5 1 10 1 0.5 0-0.5-1 10 2-12 -10-8 -6-4 -2 0 2 log(a/a ) x 10 4 0 A. Albrecht Inflation Tutorial NBI 2018 106

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 6 x 10 5 4 2 0-2 1 = 10 1-4 -6-4 -3-2 -1 0 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI 2018 107

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 6 x 10 5 4 2 0-2 Q = 1 10 1-4 -6-4 -3-2 -1 0 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI 2018 108

log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) x 10 5 6 Not at all classical! 4 2 0-2 Q = 1 10 1-4 -6-4 -3-2 -1 0 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI 2018 109

log[(r H /R H 0 )] 6 4 2 0-2 -4-6 x 10 5 Self-reproduction regime 10 1 Q = 1 Steinhardt 1982, Linde 1982, Vilenkin 1983, and (then) many others Substantial probability of fluctuating up the potential and continuing the inflationary expansion Eternal Inflation -4-3 -2-1 0 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI 2018 110

log[(r H /R H 0 )] 6 4 2 0-2 -4-6 x 10 5 Self-reproduction regime 10 1 Q = 1 Substantial probability of fluctuating up the potential and continuing the inflationary expansion Eternal Inflation Observable Universe -4-3 -2-1 0 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI 2018 111

log[(r H /R H 0 )] At end of self-reproduction our observable length scales were exponentially below the Plank length (and much smaller than that x 10 *during* self-reproduction)! 5 6 4 2 0-2 Q = 1 10 1-4 -6 4.4 ( 10 3 ) 10 l P -4-3 -2-1 0 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI 2018 112

log[(r H /R H 0 )] At formation (Hubble length crossing) observable scales were just above the Planck length 10 0-10 -20-30 -40-50 -60-70 10 l P -80-60 -50-40 -30-20 -10 0 log(a/a ) 0 (Bunch Davies Vacuum) A. Albrecht Inflation Tutorial NBI 2018 113

log[(r H /R H 0 )] 6 4 2 0-2 -4-6 x 10 5 Self-reproduction regime 10 1 Q = 1 Substantial probability of fluctuating up the potential and continuing the inflationary expansion Eternal Inflation -4-3 -2-1 0 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI 2018 114

V/M GUT 4 2.5 x 104 2 1.5 1 In self-reproduction regime, quantum fluctuations compete with classical rolling Q 0.5 0-200 -100 0 100 200 /M P A. Albrecht Inflation Tutorial NBI 2018 115

Self-reproduction is a generic feature of almost any inflaton potential: During inflation ( ) + 3H = V 3H V ( ) Q H H V = V V 2 3 3/2 ( ) V 3H ( ) A. Albrecht Inflation Tutorial NBI 2018 116

Self-reproduction is a generic feature of almost any inflaton potential: During inflation ( ) + 3H = V 3H V ( ) Q H H V = V V 2 3 3/2 ( ) V 3H ( ) for selfreproduction 1 A. Albrecht Inflation Tutorial NBI 2018 117

V/M GUT 4 2.5 x 104 2 1.5 1 In self-reproduction regime, quantum fluctuations compete with classical rolling Q Linde & Linde 0.5 0-200 -100 0 100 200 /M P A. Albrecht Inflation Tutorial NBI 2018 118

d 5R S H Self-reproduction regime Classically Rolling t = 0 A. Albrecht Inflation Tutorial NBI 2018 t 119

d 5R S H Self-reproduction regime Classically Rolling NB: shifting focus to l( t) t = 0 A. Albrecht Inflation Tutorial NBI 2018 t 120

Classicaly Roling 2 d e 5R S H Self-reproduction regime Classically Rolling New pocket (elsewhere) t = 2 R S / c H A. Albrecht Inflation Tutorial NBI 2018 t 121

3 d e 5R S H Self-reproduction regime Classically Rolling New pocket (elsewhere) t = 3 R S / c H A. Albrecht Inflation Tutorial NBI 2018 t 122

500 d e 5R S H Self-reproduction regime Classically Rolling New pocket (elsewhere) 502 r e d t = 500 R S / c H A. Albrecht Inflation Tutorial NBI 2018 t 123

Classicaly Roling 1000 d e 5R S H Self-reproduction regime New pocket (elsewhere) 1002 r e d t = 1000 R S / c H A. Albrecht Inflation Tutorial NBI 2018 t 124

1400 d e 5R S H Self-reproduction regime New pocket (elsewhere) 1402 r e d t = 1400 R S / c H A. Albrecht Inflation Tutorial NBI 2018 t 125

1395 d e 5R S H Self-reproduction regime Classically Rolling New pocket (elsewhere) 1393 r e d t = 1400 R S / c H A. Albrecht Inflation Tutorial NBI 2018 t 126

1991 d e 5R S H Self-reproduction regime Classically Rolling New pocket (elsewhere) 1989 r e d t = 2000 R S / c H A. Albrecht Inflation Tutorial NBI 2018 t 127

534395 d e 5R S Iend H RH Self-reproduction regime Classically Rolling New pocket (elsewhere) 534393 r e d A. Albrecht Inflation Tutorial NBI 2018 ( ) t = 602, 785 R S / c H t 128

534395 d e 5R S Iend H RH Reheating Self-reproduction regime New pocket (elsewhere) 534393 r e d A. Albrecht Inflation Tutorial NBI 2018 t = 2 R Iend / c H t 129

534395 d e 5R S Iend H RH Radiation Era Self-reproduction regime New pocket (elsewhere) 534393 r e d A. Albrecht Inflation Tutorial NBI 2018 t = 3.2 R Iend / c H t 130

Eternal inflation features Most of the Universe is always inflating A. Albrecht Inflation Tutorial NBI 2018 131

Eternal inflation features Most of the Universe is always inflating Leads to infinite Universe, infinitely many pocket universes. The self-reproduction phase lasts forever (globally). A. Albrecht Inflation Tutorial NBI 2018 133

Eternal inflation features Most of the Universe is always inflating Leads to infinite Universe, infinitely many pocket universes. The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. A. Albrecht Inflation Tutorial NBI 2018 136

Eternal inflation features Most of the Universe is always inflating Leads to infinite Universe, infinitely many pocket universes. The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially favored (produced in an exponentially larger region). A. Albrecht Inflation Tutorial NBI 2018 137

Eternal inflation features Most of the Universe is always inflating Leads to infinite Universe, infinitely many pocket universes. The self-reproduction phase lasts forever. Inflation Anything takes over that the Universe, can happen seems like a good theory of initial conditions. will happened infinitely Need to regulate many s times! to make (A. predictions, Guth) typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially favored (produced in an exponentially larger region). Young universe problem End of time problem Measure problems State of the art: Instead of making predictions, experts are using the data to infer the correct measure A. Albrecht Inflation Tutorial NBI 2018 141

Eternal inflation features True Most of the Universe is always inflating infinity Leads to infinite Universe, infinitely many pocket universes. needed here The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially favored (produced in an exponentially larger region). Young universe problem End of time problem Measure problems State of the art: Instead of making predictions, experts are using the data to infer the correct measure A. Albrecht Inflation Tutorial NBI 2018 142

Eternal inflation features Most of the Universe is always inflating Leads to infinite Universe, infinitely many pocket universes. needed here The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Hernley, AA & Dray True infinity Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially favored (produced in an exponentially larger region). Young universe problem End of time problem Measure problems State of the art: Instead of making predictions, experts are using the data to infer the correct measure A. Albrecht Inflation Tutorial NBI 2018 143

Eternal inflation features Multiply by 10 500 to get landscape story! True Most of the Universe is always inflating infinity Leads to infinite Universe, infinitely many pocket universes. needed here The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially favored (produced in an exponentially larger region). Young universe problem End of time problem Measure problems State of the art: Instead of making predictions, the experts are using the data to infer the correct measure A. Albrecht Inflation Tutorial NBI 2018 144

Eternal inflation features True Most of the Universe is always inflating infinity Leads to infinite Universe, infinitely many pocket universes. needed here The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially Multiple favored ( ) (produced copies of in you an in exponentially larger region). the wavefunction Young universe Page s Born problem Rule Problem End of time problem Measure problems State of the art: Instead of making predictions, the experts are using the data to infer the correct measure A. Albrecht Inflation Tutorial NBI 2018 145

Eternal inflation features True Most of the Universe is always inflating infinity Leads to infinite Universe, infinitely many pocket universes. needed here The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially Multiple favored ( ) (produced copies of in you an in exponentially larger region). the wavefunction Young universe Page s Born problem Rule Problem AA End & Phillips of time 2012: problem Be Measure careful problems about State of counting the art: Instead arguments. of making predictions, Many are just the wrong! experts are using the data to infer the A. Albrecht Inflation Tutorial NBI 2018 146 correct measure

Eternal inflation features True Most of the Universe is always inflating infinity Leads to infinite Universe, infinitely many pocket universes. needed here The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially Multiple favored ( ) (produced copies of in you an in exponentially larger region). the wavefunction Young universe Page s Born problem Rule Problem AA End & Phillips of time 2012: problem Be Measure careful problems about State of counting the art: Instead arguments. of making predictions, Many are just the wrong! experts are using the data to infer the A. Albrecht Inflation Tutorial NBI 2018 147 correct measure

Eternal inflation features True Most of the Universe is always inflating infinity Leads to infinite Universe, infinitely many pocket universes. needed here The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially favored (produced in an exponentially larger region). Young universe problem End of time problem Measure problems State of the art: Instead of making predictions, the experts are using the data to infer the correct measure A. Albrecht Inflation Tutorial NBI 2018 148

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 149

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 150

holography may limit inflation to just enough Banks and Fischler, AA, Phillips et al, Carroll etc? Phillips et al 1410.6065? A. Albrecht Inflation Tutorial NBI 2018 151

holography may limit inflation to just enough Banks and Fischler, AA, Phillips et al, Carroll etc? Phillips et al 1410.6065? A. Albrecht Inflation Tutorial NBI 2018 152

Emergence of space, EFTs? holography may limit inflation to just enough Banks and Fischler, AA, Phillips et al, Carroll etc? AA 0906.1047 AA and Sorbo, hep-th/0405270 AA 1401.7309 A. Albrecht Inflation Tutorial NBI 2018 153

Emergence of space, EFTs? Upper bound on inflation from finite entropy bound holography may limit inflation to just enough Banks and Fischler, AA, Phillips et al, Carroll etc? A. Albrecht Inflation Tutorial NBI 2018 154

Emergence of space, EFTs? holography may limit inflation to just enough Upper bound on inflation from finite entropy bound Upper bound is saturated by tunneling process that starts inflation? Banks and Fischler, AA, Phillips et al, Carroll etc A. Albrecht Inflation Tutorial NBI 2018 155

Emergence of space, EFTs? holography may limit inflation to just enough Cosmology benefits re measure and tuning issues Banks and Fischler, AA, Phillips et al, Carroll etc? A. Albrecht Inflation Tutorial NBI 2018 156

holography may limit inflation to just enough? The start of inflation (emergence of space), EFT, may be observable? Banks and Fischler, AA, Phillips et al, Carroll etc A. Albrecht Inflation Tutorial NBI 2018 157

Possible signatures of short inflation and quantum entanglement Bolis et al arxiv:1605.01008 A. Albrecht Inflation Tutorial NBI 2018 158

(In progress) Full MCMC exploration Bolis et al arxiv:1605.01008 With Andrew Arrasmith A. Albrecht Inflation Tutorial NBI 2018 159

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 160

OUTLINE 1. Big Bang basics 2. Inflation basics 3. Eternal inflation 4. An alternative to Eternal Inflation 5. Further thoughts A. Albrecht Inflation Tutorial NBI 2018 161

What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation A. Albrecht Inflation Tutorial NBI 2018 162

What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation A. Albrecht Inflation Tutorial NBI 2018 163

What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation Need a metatheory to answer this A. Albrecht Inflation Tutorial NBI 2018 164

What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation Need a metatheory to answer this No good one so far A. Albrecht Inflation Tutorial NBI 2018 165

What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation NEXT: A (popular) not good meta theory Need a metatheory to answer this No good one so far A. Albrecht Inflation Tutorial NBI 2018 166

3 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) 2 1 0-2 0 2 /M P A. Albrecht Inflation Tutorial NBI 2018 167

3 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) 2 1 0-2 0 2 /M P A. Albrecht Inflation Tutorial NBI 2018 168

3 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) 2 1 0-2 0 2 /M P A. Albrecht Inflation Tutorial NBI 2018 169

3 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) 2 1 Reasonable chance to start inflation 0-2 0 2 /M P A. Albrecht Inflation Tutorial NBI 2018 170

V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) 3 2 1 But many more field excitations here 0-2 0 2 /M P A. Albrecht Inflation Tutorial NBI 2018 171

4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) V/M GUT 3 2 1 Plus de Sitter entropy arguments give Compare with exp S P12 = exp S ( ) ( ) ( ) 0 exponential 4-2 0 M exp 2 V values /M V2 P suppression of higher 1 2 = exp S S 1 2 M = exp V M V 4 4 P P 1 2 A. Albrecht Inflation Tutorial NBI 2018 172 AA and Sorbo, hep-th/0405270

4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) V/M GUT 3 Compare with numerical solution of 2 initial 1 conditions problem Entropy arguments Compare with exp S P12 = exp S ( ) ( ) 2 East et al 1511.05143 exp( ) Braden et S1al 1604.04001 S2 Clough et al 1608.04408 4 4 MP MP = 0 4-2 give exponential 0 M exp 2 /M V2 P 1 = exp V V 1 2 suppression of higher V values A. Albrecht Inflation Tutorial NBI 2018 173

4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) V/M GUT 3 Compare with numerical solution of 2 initial 1 conditions problem Entropy arguments Compare with exp S P12 = exp S All are temporally provincial in some way ( ) ( ) 2 East et al 1511.05143 exp( ) Braden et S1al 1604.04001 S2 Clough et al 1608.04408 4 4 MP MP = 0 4-2 give exponential 0 M exp 2 /M V2 P 1 = exp V V 1 2 suppression of higher V values A. Albrecht Inflation Tutorial NBI 2018 174

What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation Not clear whether a good meta theory would favor inflation over just the SBB with correct initial conditions Need a metatheory to answer this No good one so far A. Albrecht Inflation Tutorial NBI 2018 176

S Statistical arguments No satisfactory resolution at this point. (Do we need one?) SBB What we actually believe X Today The thermodynamic arrow of time = low initial S Inflation Adding reheating and inflation seems to The past hypothesis = Fine tuning A. Albrecht Inflation Tutorial NBI 2018 177 t

Eternal inflation features True Most of the Universe is always inflating infinity Leads to infinite Universe, infinitely many pocket universes. needed here The self-reproduction phase lasts forever. Inflation takes over the Universe, seems like a good theory of initial conditions. Need to regulate s to make predictions, typically use a cutoff. For a specific time cutoff, the most recently produced pocket universes are exponentially favored (produced in an exponentially larger region). Young universe problem Or, End just of be time happy problem we Measure problems State of the art: Instead of making predictions, the experts are using the data to infer the correct measure A. Albrecht Inflation Tutorial NBI 2018 have equations to solve? 178

Cosmic Inflation: Consumers & Producers Albrecht NORDITA July 21 2017 179

https://www.aanda.org/articles/aa/full_html/2016/10/aa25898-15/aa25898-15.html fig 55 A. Albrecht Inflation Tutorial NBI 2018 180

Conclusions A) Inflation is a technical tool for connecting cosmological observables with high energy physics. Impressive successes. B) However, without a meta theory about how inflation started (and how it competes with other scenarios, such as the SBB) big questions are unresolved. C) Complex sociology as different individuals choose to give A) and B) different weight. A. Albrecht Inflation Tutorial NBI 2018 181

Conclusions A) Inflation is a technical tool for connecting cosmological observables with high energy physics. Impressive successes. B) However, without a meta theory about how inflation started (and how it competes with other scenarios, such as the SBB) big questions are unresolved. C) Complex sociology as different individuals choose to give A) and B) different weight. My priors A. Albrecht Inflation Tutorial NBI 2018 182