Cosmic Inflation Tutorial
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1 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
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
3 Cosmic Inflation: Concrete technical idea with great phenomenology Couched in the language of solving tuning problems Big open questions A. Albrecht Inflation Tutorial NBI
4 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
5 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. Priors!! A. Albrecht Inflation Tutorial NBI
6 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. Priors!! Q A. Albrecht Inflation Tutorial NBI
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
8 Cosmic Inflation: Concrete technical idea with great phenomenology Couched in the language of solving tuning problems Big open questions A. Albrecht Inflation Tutorial NBI
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
10 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
11 Einstein equation + Homogeneity & Isotropy Friedmann Eqn. H 2 2 a 8 = = G a 3 ( ) k r m DE A. Albrecht Inflation Tutorial NBI
12 Friedmann Eqn. H 2 2 a 8 = = G a 3 ( ) k r m DE A. Albrecht Inflation Tutorial NBI
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) A. Albrecht Inflation Tutorial NBI
14 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
15 Friedmann Eqn. a 2 H 2 2 a 8 = = G a 3 ( ) k r m DE Curvature Scale factor A. Albrecht Inflation Tutorial NBI
16 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
17 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
18 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
19 log(/ c 0 ) Evolution of Cosmic Matter r m log(a/a 0 ) Today A. Albrecht Inflation Tutorial NBI
20 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
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
22 Time The History of the Universe Image of the Last Scattering Surface or edge of opaqueness High Energy & Temp A. Albrecht Inflation Tutorial NBI
23 log(/ c 0 ) The curvature feature/ problem k r m log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
24 log(/ c 0 ) The curvature feature/ problem k r m ! log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
25 log(/ c 0 ) The curvature feature/ problem k r m 20 0! log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
26 log(/ c 0 ) The curvature feature/ problem r m k 20 0! log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
27 log(/ c 0 ) The curvature feature/ problem r m k log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
28 log(/ c 0 ) The curvature feature/ problem! r m k log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
29 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
30 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
31 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
32 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 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 Univ bh Max Univ I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI
33 log(/ c 0 ) The monopole problem Mono r m log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
34 log(/ c 0 ) The monopole problem Mono r m ! log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
35 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
36 i SBB Horizon t= 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
37 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
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
39 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
40 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
41 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
42 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
43 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
44 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
45 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 V A. Albrecht Inflation Tutorial NBI
46 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 V A. Albrecht Inflation Tutorial NBI
47 log(/ c 0 ) Add a period of Inflation: I r m log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
48 log(/ c 0 ) With inflation, initially large curvature is OK: I r 80 m 60 k log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
49 log(/ c 0 ) With inflation, early production of large amounts of non-relativistic matter (monopoles) is ok : I r 80 m 60 Mono log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
50 log(/ c 0 ) With inflation, early production of large amounts of non-relativistic matter (monopoles) is ok : I r 80 m 60 Mono log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
51 Inflation detail: log(/ c 0 ) KE V r /M P log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
52 log(/ c 0 ) Inflation detail: KE V 4 V/M GUT V ( ) = m /M P 0.5 r /M P log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
53 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
54 log(r H /R H 0 ) R H c 1 H Tot 1/2 R H log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
55 log(r H /R H 0 ) R i H c 1 Hi i 1/2 I R H r R H m R H R H log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
56 log(r H /R H 0 ) R i H c 1 Hi i 1/2 I R H r R H m R H R H Tot R H log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
57 log(r H /R H 0 ) R H c 1 H Tot 1/2 R H log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
58 log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length End of inflation log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
59 log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length End of reheating log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
60 log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length Weak Scale log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
61 log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length BBN log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
62 log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length Radiation- Matter equality log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
63 log[(r H /R H 0 ) -1 ] Evolution of Cosmic Length Today log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
64 log(r H /R H 0 ) Perturbations from inflation log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
65 log(r H /R H 0 ) Perturbations from inflation Here log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
66 log(r H /R H 0 ) Perturbations from inflation H Here Here log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
67 log(r H /R H 0 ) H Here Here log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
68 log(r H /R H 0 ) H Here Here log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
69 log(r H /R H 0 ) H Here Here Short wavelength QFT modes taken to be in vacuum state (the Bunch Davies -70 Vacuum ) log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
70 log(/ c 0 ) Inflation detail: KE V 4 V/M GUT V ( ) = m /M P 0.5 r /M P log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
71 log(/ c 0 ) Inflation detail: KE V 4 V/M GUT V ( ) = m /M P 0.5 r /M P 0 m = 810 to give log(a/a 0 ) 12 GeV A. Albrecht Inflation Tutorial NBI
72 log(/ c 0 ) Inflation detail: KE V 4 V/M GUT V ( ) = m /M P 0.5 r /M P log(a/a 0 ) A. Albrecht Inflation Tutorial NBI
73 log(r H /R H 0 ) H Here Here log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
74 arxiv: v1 A. Albrecht Inflation Tutorial NBI
75 Planck CMB data Inflation theory A. Albrecht Inflation Tutorial NBI
76 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 ( ) V ( ) V ( ) V ( ) d da Which implies p = 0 w=-1 a~ e Ht Inflation I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI
77 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
78 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
79 i Inflation Horizon: Inflation starts Inflation ends Here & Now I.0 What is Cosmic Inflation? A. Albrecht Inflation Tutorial NBI
80 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
81 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
82 Wtotal=1 WMAP Bennett et al Feb A. Albrecht Inflation Tutorial NBI
83 Temperature Power Characteristic oscillations in the CMB power WMAP Inflation Active models Angular scale Adapted from Bennett et al Feb A. Albrecht Inflation Tutorial NBI
84 Nearly scale invariant perturbation spectrum WMAP k ( ) H= k = Ak 1 ns Bennett et al Feb A. Albrecht Inflation Tutorial NBI
85 Characteristic Gravity wave, CMB Polarization etc WMAP TxE polarization power Inflation Active models Bennett et al Feb A. Albrecht Inflation Tutorial NBI
86 fig 55 A. Albrecht Inflation Tutorial NBI
87 What happened before inflation? A. Albrecht Inflation Tutorial NBI
88 What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation A. Albrecht Inflation Tutorial NBI
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
90 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
91 Eternal inflation A. Albrecht Inflation Tutorial NBI
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 = measures the importance of quantum fluctuations in the field evolution A. Albrecht Inflation Tutorial NBI
93 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
94 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
95 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
96 V/M GUT If this region produced our observable universe /M P A. Albrecht Inflation Tutorial NBI
97 V/M GUT If this region produced our observable universe /M P A. Albrecht Inflation Tutorial NBI
98 2.5 V/M GUT It seems reasonable to assume the field was rolling up here beforehand (classical extrapolation) /M P A. Albrecht Inflation Tutorial NBI
99 log[(r H /R H 0 )] Evolution of Cosmic Length log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
100 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
101 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
102 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
103 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
104 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) x log(a/a ) 0 A. Albrecht Inflation Tutorial NBI
105 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 6 x log(a/a ) 0 x 10 4 A. Albrecht Inflation Tutorial NBI
106 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) x log(a/a ) x A. Albrecht Inflation Tutorial NBI
107 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 6 x = log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI
108 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) 6 x Q = log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI
109 log[(r H /R H 0 )] Evolution of Cosmic Length (zooming out) x Not at all classical! Q = log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI
110 log[(r H /R H 0 )] 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 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI
111 log[(r H /R H 0 )] 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 log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI
112 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)! Q = ( 10 3 ) 10 l P log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI
113 log[(r H /R H 0 )] At formation (Hubble length crossing) observable scales were just above the Planck length l P log(a/a ) 0 (Bunch Davies Vacuum) A. Albrecht Inflation Tutorial NBI
114 log[(r H /R H 0 )] x 10 5 Self-reproduction regime 10 1 Q = 1 Substantial probability of fluctuating up the potential and continuing the inflationary expansion Eternal Inflation log(a/a ) 0 x 10 5 A. Albrecht Inflation Tutorial NBI
115 V/M GUT x In self-reproduction regime, quantum fluctuations compete with classical rolling Q /M P A. Albrecht Inflation Tutorial NBI
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 ( ) A. Albrecht Inflation Tutorial NBI
117 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
118 V/M GUT x In self-reproduction regime, quantum fluctuations compete with classical rolling Q Linde & Linde /M P A. Albrecht Inflation Tutorial NBI
119 d 5R S H Self-reproduction regime Classically Rolling t = 0 A. Albrecht Inflation Tutorial NBI 2018 t 119
120 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
121 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
122 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
123 500 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
124 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
125 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
126 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
127 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
128 d e 5R S Iend H RH Self-reproduction regime Classically Rolling New pocket (elsewhere) r e d A. Albrecht Inflation Tutorial NBI 2018 ( ) t = 602, 785 R S / c H t 128
129 d e 5R S Iend H RH Reheating Self-reproduction regime New pocket (elsewhere) r e d A. Albrecht Inflation Tutorial NBI 2018 t = 2 R Iend / c H t 129
130 d e 5R S Iend H RH Radiation Era Self-reproduction regime New pocket (elsewhere) r e d A. Albrecht Inflation Tutorial NBI 2018 t = 3.2 R Iend / c H t 130
131 Eternal inflation features Most of the Universe is always inflating A. Albrecht Inflation Tutorial NBI
132 Eternal inflation features Most of the Universe is always inflating Leads to infinite Universe, infinitely many pocket universes. The self-reproduction phase lasts forever. A. Albrecht Inflation Tutorial NBI
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 (globally). A. Albrecht Inflation Tutorial NBI
134 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. A. Albrecht Inflation Tutorial NBI
135 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. A. Albrecht Inflation Tutorial NBI
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. A. Albrecht Inflation Tutorial NBI
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 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
138 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). Young universe problem End of time problem Measure problems A. Albrecht Inflation Tutorial NBI
139 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). 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
140 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). 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
141 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
142 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
143 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
144 Eternal inflation features Multiply by 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
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 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
146 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 correct measure
147 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 correct measure
148 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
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
150 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
151 holography may limit inflation to just enough Banks and Fischler, AA, Phillips et al, Carroll etc? Phillips et al ? A. Albrecht Inflation Tutorial NBI
152 holography may limit inflation to just enough Banks and Fischler, AA, Phillips et al, Carroll etc? Phillips et al ? A. Albrecht Inflation Tutorial NBI
153 Emergence of space, EFTs? holography may limit inflation to just enough Banks and Fischler, AA, Phillips et al, Carroll etc? AA AA and Sorbo, hep-th/ AA A. Albrecht Inflation Tutorial NBI
154 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
155 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
156 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
157 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
158 Possible signatures of short inflation and quantum entanglement Bolis et al arxiv: A. Albrecht Inflation Tutorial NBI
159 (In progress) Full MCMC exploration Bolis et al arxiv: With Andrew Arrasmith A. Albrecht Inflation Tutorial NBI
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
161 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
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
163 What happened before inflation? Related to some more contentious topics: How well does inflation solve tuning problems? Eternal inflation A. Albrecht Inflation Tutorial NBI
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 A. Albrecht Inflation Tutorial NBI
165 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
166 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
167 3 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) /M P A. Albrecht Inflation Tutorial NBI
168 3 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) /M P A. Albrecht Inflation Tutorial NBI
169 3 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) /M P A. Albrecht Inflation Tutorial NBI
170 3 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) 2 1 Reasonable chance to start inflation /M P A. Albrecht Inflation Tutorial NBI
171 V/M GUT 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) But many more field excitations here /M P A. Albrecht Inflation Tutorial NBI
172 4 Beware temporal provincialism : Equipartition argument (equally likely anywhere on potential) V/M GUT Plus de Sitter entropy arguments give Compare with exp S P12 = exp S ( ) ( ) ( ) 0 exponential 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 AA and Sorbo, hep-th/
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 ( ) ( ) 2 East et al exp( ) Braden et S1al S2 Clough et al MP MP = 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
174 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 exp( ) Braden et S1al S2 Clough et al MP MP = 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
175 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
176 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
177 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 t
178 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
179 Cosmic Inflation: Consumers & Producers Albrecht NORDITA July
180 fig 55 A. Albrecht Inflation Tutorial NBI
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. A. Albrecht Inflation Tutorial NBI
182 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
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