Inflation, infinity, equilibrium and the observable Universe Andreas Albrecht UC Davis UCD Colloquium October 3, A. UCD 10/3/11

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5 Cosmic Inflation:  Great phenomenology, but  Original goal of explaining why the cosmos is *likely* to take the form we observe has proven very difficult to realize.

A. UCD 10/3/116 Cosmic Inflation:  Great phenomenology, but  Original goal of explaining why the cosmos is *likely* to take the form we observe has proven very difficult to realize. This Talk

A. UCD 10/3/117 Cosmic Inflation:  Great phenomenology, but  Original goal of explaining why the cosmos is *likely* to take the form we observe has proven very difficult to realize.  OR: Just be happy we have equations to solve?

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. UCD 10/3/118

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. UCD 10/3/119

Friedmann Eqn. A. UCD 10/3/1110

Friedmann Eqn. Curvature A. UCD 10/3/1111

Friedmann Eqn. Curvature Relativistic Matter A. UCD 10/3/1112

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter A. UCD 10/3/1113

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter Dark Energy A. UCD 10/3/1114

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The curvature feature/“problem” A. UCD 10/3/1118

! The curvature feature/“problem” A. UCD 10/3/1119

! The curvature feature/“problem” A. UCD 10/3/1120

! The curvature feature/“problem” A. UCD 10/3/1121

The curvature feature/“problem” A. UCD 10/3/1122

! The curvature feature/“problem” A. UCD 10/3/1123

The monopole “problem” A. UCD 10/3/1124

! The monopole “problem” A. UCD 10/3/1125

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter Dark Energy A. UCD 10/3/1126

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter Dark Energy Now add cosmic inflation Inflaton A. UCD 10/3/1127

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter Dark Energy Now add cosmic inflation Inflaton A. UCD 10/3/1128

The inflaton: ~Homogeneous scalar field obeying All potentials have a “low roll” (overdamped) regime where Cosmic damping Coupling to ordinary matter A. UCD 10/3/1129

The inflaton: ~Homogeneous scalar field obeying All potentials have a “low roll” (overdamped) regime where Cosmic damping Coupling to ordinary matter A. UCD 10/3/1130

Add a period of Inflation: A. UCD 10/3/1131

With inflation, initially large curvature is OK: A. UCD 10/3/1132

With inflation, early production of large amounts of non-relativistic matter (monopoles) is ok : A. UCD 10/3/1133

Inflation detail: A. UCD 10/3/1134

Inflation detail: A. UCD 10/3/1135

Hubble Length A. UCD 10/3/1136

Hubble Length A. UCD 10/3/1137 (aka )

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End of inflation A. UCD 10/3/1149

End of reheating A. UCD 10/3/1150

Weak Scale A. UCD 10/3/1151

BBN A. UCD 10/3/1152

Radiation- Matter equality A. UCD 10/3/1153

Today A. UCD 10/3/1154

Perturbations from inflation comoving A. UCD 10/3/1155

Here Perturbations from inflation comoving A. UCD 10/3/1156

Here Perturbations from inflation comoving A. UCD 10/3/1157

Here comoving A. UCD 10/3/1158

Here comoving A. UCD 10/3/1159

Inflation detail: A. UCD 10/3/1160

Inflation detail: to give A. UCD 10/3/1161

Here comoving A. UCD 10/3/1162

Brown et al. Astrophys.J.705: ,2009 A. UCD 10/3/1163

Brown et al. Astrophys.J.705: ,2009 A. UCD 10/3/1164

A. UCD 10/3/1165 Keiser et al. 2011

A. UCD 10/3/1166 Keiser et al. 2011

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. UCD 10/3/1167

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. UCD 10/3/1168

Does inflation make the SBB natural? How easy is it to get inflation to start? What happened before inflation? A. UCD 10/3/1169

Quantum fluctuations during slow roll: A region of one field coherence length ( ) gets a new quantum contribution to the field value from an uncorrelated commoving mode of size in a time leading to a (random) quantum rate of change: Thus measures the importance of quantum fluctuations in the field evolution 70A. UCD 10/3/11

Quantum fluctuations during slow roll: A region of one field coherence length ( ) gets a new quantum contribution to the field value from an uncorrelated commoving mode of size in a time leading to a (random) quantum rate of change: Thus measures the importance of quantum fluctuations in the field evolution ( ) 71A. UCD 10/3/11

Quantum fluctuations during slow roll: A region of one field coherence length ( ) gets a new quantum contribution to the field value from an uncorrelated commoving mode of size in a time leading to a (random) quantum rate of change: Thus measures the importance of quantum fluctuations in the field evolution ( ) For realistic perturbations the evolution is very classical 72A. UCD 10/3/11

If this region “produced our observable universe”… A. UCD 10/3/1173

It seems reasonable to assume the field was rolling up here beforehand (classical extrapolation) A. UCD 10/3/1174

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Not at all classical! A. UCD 10/3/1185

Self-reproduction regime Substantial probability of fluctuating up the potential and continuing the inflationary expansion  “Eternal Inflation” A. UCD 10/3/1186 Linde 1986 and (then) many others

Self-reproduction regime Substantial probability of fluctuating up the potential and continuing the inflationary expansion  “Eternal Inflation” A. UCD 10/3/1187

Self-reproduction regime Substantial probability of fluctuating up the potential and continuing the inflationary expansion  “Eternal Inflation” Observable Universe A. UCD 10/3/1188

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Self-reproduction regime Substantial probability of fluctuating up the potential and continuing the inflationary expansion  “Eternal Inflation” A. UCD 10/3/1191

In self-reproduction regime, quantum fluctuations compete with classical rolling A. UCD 10/3/1192 Q

A. UCD 10/3/1193 Self-reproduction is a generic feature of any inflaton potential: During inflation

A. UCD 10/3/1194 Self-reproduction is a generic feature of any inflaton potential: During inflation for self- reproduction

In self-reproduction regime, quantum fluctuations compete with classical rolling A. UCD 10/3/1195 Q Linde & Linde

Classically Rolling Self-reproduction regime 96A. UCD 10/3/11

New pocket (elsewhere) Classically Rolling Self-reproduction regime 97A. UCD 10/3/11

New pocket (elsewhere) Classically Rolling Self-reproduction regime 98A. UCD 10/3/11

New pocket (elsewhere) Classically Rolling Self-reproduction regime 99A. UCD 10/3/11

New pocket (elsewhere) Classically Rolling Self-reproduction regime 100A. UCD 10/3/11

New pocket (elsewhere) Self-reproduction regime 101A. UCD 10/3/11

New pocket (elsewhere) Classically Rolling Self-reproduction regime 102A. UCD 10/3/11

New pocket (elsewhere) Classically Rolling Self-reproduction regime 103A. UCD 10/3/11

New pocket (elsewhere) Classically Rolling Self-reproduction regime 104A. UCD 10/3/11

New pocket (elsewhere) Reheating Self-reproduction regime 105A. UCD 10/3/11

New pocket (elsewhere) Radiation Era Self-reproduction regime 106A. UCD 10/3/11

Eternal inflation features Most of the Universe is always inflating A. UCD 10/3/11107

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. UCD 10/3/11108

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. UCD 10/3/11109

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. UCD 10/3/11110

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 Young universe problem  End of time problem  Measure problems 113A. UCD 10/3/11

 Young universe problem  End of time problem  Measure problems 114A. UCD 10/3/11  State of the art: Instead of making predictions, the experts are using the data to infer the “correct measure”

 Young universe problem  End of time problem  Measure problems 115A. UCD 10/3/11  State of the art: Instead of making predictions, the experts are using the data to infer the “correct measure”

 Young universe problem  End of time problem  Measure problems 116A. UCD 10/3/11  State of the art: Instead of making predictions, the experts are using the data to infer the “correct measure” “True infinity” needed here

 Young universe problem  End of time problem  Measure problems 117A. UCD 10/3/11  State of the art: Instead of making predictions, the experts are using the data to infer the “correct measure” “True infinity” needed here Multiply by to get landscape story!

 Young universe problem  End of time problem  Measure problems 118A. UCD 10/3/11  State of the art: Instead of making predictions, the experts are using the data to infer the “correct measure” “True infinity” needed here  Multiple (∞) copies of “you” in the wavefunction  Page’s “Born Rule Crisis”

 Young universe problem  End of time problem  Measure problems 119A. UCD 10/3/11  State of the art: Instead of making predictions, the experts are using the data to infer the “correct measure” “True infinity” needed here

A problem has been detected and your calculation has been shut down to prevent damage RELATIVE_PROBABILITY_OVERFLOW If this is the first time you have seen this stop error screen, restart your calculation. If this screen appears again, follow these steps: Check to make sure all extrapolations are justified and equations are valid. If you are new to this calculation consult your theory manufacturer for any measure updates you might need. If the problems continue, disable or remove features of the theory that cause the overflow error. Disable BS options such as self- reproduction or infinite time. If you need to use safe mode to remove or disable components, restart your computation and utilize to select holographic options. 120A. UCD 10/3/11

 Young universe problem  End of time problem  Measure problems 121A. UCD 10/3/11  State of the art: Instead of making predictions, the experts are using the data to infer the “correct measure” “True infinity” needed here Or, just be happy we have equations to solve?

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. UCD 10/3/11122

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. UCD 10/3/11123

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A. UCD 10/3/11130 AA: arXiv: AA: arXiv: AA & Sorbo: hep-th/

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domination A. UCD 10/3/11135

domination Asymptotic behavior  de Sitter Space A. UCD 10/3/11136

The de Sitter horizon Past horizon of observation event at this time 137A. UCD 10/3/11 Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.

The de Sitter horizon Past horizon of observation event at this time 138A. UCD 10/3/11 Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.

The de Sitter horizon Past horizon of any observation event deep in the de Sitter era 139A. UCD 10/3/11 Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.

Past horizon of any observation event deep in the de Sitter era Future horizon of event at reheating (distance photon has traveled, in SBB). A. UCD 10/3/11140 Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.

Implications of the de Sitter horizon Maximum entropy Gibbons-Hawking Temperature Gibbons & Hawking 1977 A. UCD 10/3/11141

“De Sitter Space: The ultimate equilibrium for the universe? Horizon A. UCD 10/3/11142

Banks & Fischler & Dyson et al. Implications of the de Sitter horizon Maximum entropy Gibbons-Hawking Temperature Only a finite volume ever observed If is truly constant: Cosmology as fluctuating Eqm. Maximum entropy finite Hilbert space of dimension A. UCD 10/3/11143

Banks & Fischler & Dyson et al. Implications of the de Sitter horizon Maximum entropy Gibbons-Hawking Temperature Only a finite volume ever observed If is truly constant: Cosmology as fluctuating Eqm.? Maximum entropy finite Hilbert space of dimension A. UCD 10/3/11144 dSE cosmology

A. UCD 10/3/11145 Equilibrium Cosmology

Rare Fluctuation A. UCD 10/3/11146

Rare Fluctuation A. UCD 10/3/11147

Concept: Realization: “de Sitter Space” A. UCD 10/3/11148

Rare Fluctuation A. UCD 10/3/11149

A. UCD 10/3/11150 Fluctuating from dSE to inflation : The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Guth-Farhi process” A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton. Rate is well approximated by the rate of seed formation: Seed mass:

A. UCD 10/3/11151 Fluctuating from dSE to inflation : The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Guth-Farhi process” A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton. Rate is well approximated by the rate of seed formation: Seed mass: Small seed can produce an entire universe  Evade “Boltzmann Brain” problem

A. UCD 10/3/11152 Fluctuating from dSE to inflation : The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Guth-Farhi process” A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton. Rate is well approximated by the rate of seed formation: Seed mass: See important new work on G-F process by Andrew Ulvestad & AA

degrees of freedom temporarily break off to form baby universe: A. UCD 10/3/11153 time Eqm. Seed Fluctuation Tunneling Evolution Inflation Radiation Matter de Sitter Recombination

A. UCD 10/3/11154 Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

A. UCD 10/3/11155 Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

A. UCD 10/3/11156 Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

A. UCD 10/3/11157 This much inflation fills one de Sitter horizon

A. UCD 10/3/11158 This much inflation fills more than one de Sitter horizon, generating total entropy and affecting regions beyond the horizon of the observer

A. UCD 10/3/11159 In dSE cosmology this region is unphysical. Breakdown of continuum field theory prevents inflation from filling more than one de Sitter horizon

A. UCD 10/3/11160 In dSE cosmology this region is unphysical. Breakdown of continuum field theory prevents inflation from filling more than one de Sitter horizon Equivalent to Banks-Fischler holographic constraint on number of e-foldings of inflation (D Phillips 2011)

A. UCD 10/3/11161 Fluctuating from dSE to inflation : The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Guth-Farhi process” A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton. Rate is well approximated by the rate of seed formation Seed mass: Large exponentially favored  saturation of dSE bound

A. UCD 10/3/11162 dSE bound on inflation given by past horizon

A. UCD 10/3/11163 dSE bound on inflation given by past horizon A variety of inflation models, all saturating the dSE bound

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. UCD 10/3/11164

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. UCD 10/3/11165

A. UCD 10/3/11166 dSE Cosmology and cosmic curvature The Guth-Farhi process starts inflation with an initial curvature set by the curvature of the Guth-Farhi Bubble Inflation dilutes the curvature, but dSE cosmology has a minimal amount of inflation

Friedmann Eqn. A. UCD 10/3/11167

A. UCD 10/3/11168 Banks & Fischler & Dyson et al. Evolution of curvature radius

A. UCD 10/3/11169 Curvature radius set by initial curvature Banks & Fischler & Dyson et al. Evolution of curvature radius

A. UCD 10/3/11170 A variety of inflation models, all saturating the dSE bound Curvature radius set by initial curvature Evolution of curvature radius

A. UCD 10/3/11171 A variety of inflation models, all saturating the dSE bound Curvature radius set by initial curvature is given by this gap Evolution of curvature radius

A. UCD 10/3/11172 AA: arXiv:

A. UCD 10/3/11173 dSE Cosmology and cosmic curvature The Guth-Farhi process starts inflation with an initial curvature set by the curvature of the Guth-Farhi bubble Inflation dilutes the curvature, but dSE cosmology has a minimal amount of inflation

A. UCD 10/3/11174 Image by Surhud More Predicted from dSE cosmology is: Independent of almost all details of the cosmology Just consistent with current observations Will easily be detected by future observations

A. UCD 10/3/11175 Image by Surhud More Predicted from dSE cosmology is: Independent of almost all details of the cosmology Just consistent with current observations Will easily be detected by future observations Work in progress on expected values of (Andrew Ulvestad & AA)

A. UCD 10/3/11176 Conclusions The search for a “big picture” of the Universe that explains why the region we observe should take this form has proven challenging, but has generated exciting ideas. We know we can do science with the Universe It appears that there is something right about cosmic inflation dSE cosmology offers a finite alternative to the extravagant (and problematic) infinities of eternal inflation Predictions of observable levels of cosmic curvature from dSE cosmology will give an important future test

A. UCD 10/3/11177 Conclusions The search for a “big picture” of the Universe that explains why the region we observe should take this form has proven challenging, but has generated exciting ideas. We know we can do science with the Universe It appears that there is something right about cosmic inflation dSE cosmology offers a finite alternative to the extravagant (and problematic) infinities of eternal inflation Predictions of observable levels of cosmic curvature from dSE cosmology will give an important future test