Inflation, infinity, equilibrium and the observable Universe Andreas Albrecht UC Davis KIPAC Seminar Jan A. Stanford Jan

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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. Stanford Jan 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. Stanford Jan 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. Stanford Jan

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. Stanford Jan

Friedmann Eqn. A. Stanford Jan

Friedmann Eqn. A. Stanford Jan

Friedmann Eqn. A. Stanford Jan Hubble parameter (“constant”, because today it takes ~10Billion years to change appreciable)

Friedmann Eqn. A. Stanford Jan Hubble parameter (“constant”, because today it takes ~10Billion years to change appreciable) “Scale factor”

Friedmann Eqn. Curvature A. Stanford Jan “Scale factor”

Friedmann Eqn. Relativistic Matter A. Stanford Jan Curvature “Scale factor”

Friedmann Eqn. Relativistic Matter Non-relativistic Matter A. Stanford Jan Curvature “Scale factor”

Friedmann Eqn. Relativistic Matter Non-relativistic Matter Dark Energy A. Stanford Jan Curvature “Scale factor”

A. Stanford Jan Evolution of Cosmic Matter

A. Stanford Jan Evolution of Cosmic Matter

A. Stanford Jan Evolution of Cosmic Matter

The curvature feature/“problem” A. Stanford Jan

! The curvature feature/“problem” A. Stanford Jan

! The curvature feature/“problem” A. Stanford Jan

! The curvature feature/“problem” A. Stanford Jan

The curvature feature/“problem” A. Stanford Jan

! The curvature feature/“problem” A. Stanford Jan

The monopole “problem” A. Stanford Jan

! The monopole “problem” A. Stanford Jan

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter Dark Energy A. Stanford Jan

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter Dark Energy Now add cosmic inflation Inflaton A. Stanford Jan

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter Dark Energy Now add cosmic inflation Inflaton A. Stanford Jan 

Friedmann Eqn. Curvature Relativistic Matter Non-relativistic Matter Dark Energy Now add cosmic inflation Inflaton A. Stanford Jan

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

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

Add a period of Inflation: A. Stanford Jan

With inflation, initially large curvature is OK: A. Stanford Jan

With inflation, early production of large amounts of non-relativistic matter (monopoles) is ok : A. Stanford Jan

With inflation, early production of large amounts of non-relativistic matter (monopoles) is ok : A. Stanford Jan

Inflation detail: A. Stanford Jan

Inflation detail: A. Stanford Jan

Hubble Length A. Stanford Jan

Hubble Length A. Stanford Jan (aka )

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End of inflation A. Stanford Jan Evolution of Cosmic Length

End of reheating A. Stanford Jan Evolution of Cosmic Length

Weak Scale A. Stanford Jan Evolution of Cosmic Length

BBN A. Stanford Jan Evolution of Cosmic Length

Radiation- Matter equality A. Stanford Jan Evolution of Cosmic Length

Today A. Stanford Jan Evolution of Cosmic Length

Perturbations from inflation comoving A. Stanford Jan

Here Perturbations from inflation comoving A. Stanford Jan

Here Perturbations from inflation comoving A. Stanford Jan

Here comoving A. Stanford Jan

Here comoving A. Stanford Jan

Inflation detail: A. Stanford Jan

Inflation detail: to give A. Stanford Jan

Here comoving A. Stanford Jan

A. Stanford Jan arXiv: v1

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. Stanford Jan

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. Stanford Jan

Does inflation make the SBB natural? How easy is it to get inflation to start? What happened before inflation? A. Stanford Jan

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 72A. Stanford Jan

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 ( ) 73A. Stanford Jan

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 74A. Stanford Jan

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 75A. Stanford Jan (But not as classical as most classical things we know!)

If this region “produced our observable universe”… A. Stanford Jan

It seems reasonable to assume the field was rolling up here beforehand (classical extrapolation) A. Stanford Jan

A. Stanford Jan Evolution of Cosmic Length

A. Stanford Jan Evolution of Cosmic Length (zooming out)

A. Stanford Jan Evolution of Cosmic Length (zooming out)

A. Stanford Jan Evolution of Cosmic Length (zooming out)

A. Stanford Jan Evolution of Cosmic Length (zooming out)

A. Stanford Jan Evolution of Cosmic Length (zooming out)

A. Stanford Jan Evolution of Cosmic Length (zooming out)

A. Stanford Jan Evolution of Cosmic Length (zooming out)

A. Stanford Jan Evolution of Cosmic Length (zooming out)

A. Stanford Jan Evolution of Cosmic Length (zooming out)

Not at all classical! A. Stanford Jan Evolution of Cosmic Length (zooming out)

Self-reproduction regime Substantial probability of fluctuating up the potential and continuing the inflationary expansion  “Eternal Inflation” A. Stanford Jan Steinhardt 1982, Linde 1982, Vilenkin 1983, and (then) many others

Self-reproduction regime Substantial probability of fluctuating up the potential and continuing the inflationary expansion  “Eternal Inflation” Observable Universe A. Stanford Jan

A. Stanford Jan At end of self-reproduction our observable length scales were exponentially below the Plank length (and much smaller than that *during* self-reproduction)!

A. Stanford Jan At “formation” (Hubble length crossing) observable scales were just above the Planck length (Bunch Davies Vacuum)

Self-reproduction regime Substantial probability of fluctuating up the potential and continuing the inflationary expansion  “Eternal Inflation” A. Stanford Jan

In self-reproduction regime, quantum fluctuations compete with classical rolling A. Stanford Jan Q

A. Stanford Jan Self-reproduction is a generic feature of almost any inflaton potential: During inflation

A. Stanford Jan Self-reproduction is a generic feature of almost any inflaton potential: During inflation for self- reproduction

In self-reproduction regime, quantum fluctuations compete with classical rolling A. Stanford Jan Q Linde & Linde

Classically Rolling Self-reproduction regime 98A. Stanford Jan

Classically Rolling Self-reproduction regime 99A. Stanford Jan NB: shifting focus to

New pocket (elsewhere) Classically Rolling Self-reproduction regime 100A. Stanford Jan

New pocket (elsewhere) Classically Rolling Self-reproduction regime 101A. Stanford Jan

New pocket (elsewhere) Classically Rolling Self-reproduction regime 102A. Stanford Jan

New pocket (elsewhere) Classically Rolling Self-reproduction regime 103A. Stanford Jan

New pocket (elsewhere) Self-reproduction regime 104A. Stanford Jan

New pocket (elsewhere) Classically Rolling Self-reproduction regime 105A. Stanford Jan

New pocket (elsewhere) Classically Rolling Self-reproduction regime 106A. Stanford Jan

New pocket (elsewhere) Classically Rolling Self-reproduction regime 107A. Stanford Jan

New pocket (elsewhere) Reheating Self-reproduction regime 108A. Stanford Jan

New pocket (elsewhere) Radiation Era Self-reproduction regime 109A. Stanford Jan

Eternal inflation features Most of the Universe is always inflating A. Stanford Jan

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. Stanford Jan

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. Stanford Jan

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. Stanford Jan

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. Stanford Jan

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 Young universe problem  End of time problem  Measure problems 117A. Stanford Jan

 Young universe problem  End of time problem  Measure problems 118A. Stanford Jan  State of the art: Instead of making predictions, experts are using the data to infer the “correct measure”

 Young universe problem  End of time problem  Measure problems 119A. Stanford Jan  State of the art: Instead of making predictions, experts are using the data to infer the “correct measure”

 Young universe problem  End of time problem  Measure problems 120A. Stanford Jan  State of the art: Instead of making predictions, experts are using the data to infer the “correct measure” “True infinity” needed here

 Young universe problem  End of time problem  Measure problems 121A. Stanford Jan  State of the art: Instead of making predictions, experts are using the data to infer the “correct measure” “True infinity” needed here Hernley, AA & Dray in prep

 Young universe problem  End of time problem  Measure problems 122A. Stanford Jan  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 123A. Stanford Jan  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 Problem”

 Young universe problem  End of time problem  Measure problems 124A. Stanford Jan  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 Problem” AA & Phillips 2012: “All probabilities are quantum”

 Young universe problem  End of time problem  Measure problems 125A. Stanford Jan  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 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. 126A. Stanford Jan

 Young universe problem  End of time problem  Measure problems 127A. Stanford Jan  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. Stanford Jan

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. Stanford Jan

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A. Stanford Jan AA: arXiv: AA: arXiv: AA & Sorbo: hep-th/

A. Stanford Jan Evolution of Cosmic Length

A. Stanford Jan Evolution of Cosmic Length

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domination A. Stanford Jan

domination Asymptotic behavior  de Sitter Space A. Stanford Jan

The de Sitter horizon Past horizon of observation event at this time 143A. Stanford Jan 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 144A. Stanford Jan 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 145A. Stanford Jan 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. Stanford Jan 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. Stanford Jan

“De Sitter Space: The ultimate equilibrium for the universe? Horizon A. Stanford Jan

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. Stanford Jan

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. Stanford Jan dSE cosmology

A. Stanford Jan Equilibrium Cosmology

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

Rare Fluctuation A. Stanford Jan

Rare Fluctuation A. Stanford Jan

Rare Fluctuation A. Stanford Jan Move Ergodicity to hidden degrees of freedom (we *know* state counting arguments do note apply to the observable universe) AA in prep

Concept: Realization: “de Sitter Space” A. Stanford Jan

Rare Fluctuation A. Stanford Jan

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

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

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

degrees of freedom temporarily break off to form baby universe: A. Stanford Jan time Eqm. Seed Fluctuation Tunneling Evolution Inflation Radiation Matter de Sitter Recombination

degrees of freedom temporarily break off to form baby universe: A. Stanford Jan time Eqm. Seed Fluctuation Tunneling Evolution Inflation Radiation Matter de Sitter Recombination “Right Timescale”

A. Stanford Jan Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

A. Stanford Jan Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

A. Stanford Jan Implications of finite Hilbert space Recurrences Eqm. Breakdown of continuum field theory

A. Stanford Jan This much inflation fills one de Sitter horizon

A. Stanford Jan This much inflation fills more than one de Sitter horizon, generating total entropy and affecting regions beyond the horizon of the observer

A. Stanford Jan In dSE cosmology this region is unphysical. Breakdown of effective field theory prevents inflation from filling more than one de Sitter horizon

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

To get eternal inflation, we made what we thought was a simple extrapolation, but wound up with a highly problematic theory A. Stanford Jan Q

dSE: The extrapolation that leads to eternal inflation is naïve, in that it neglects the breakdown of effective field theory. dSE uses holographic arguments to estimate this breakdown. A. Stanford Jan Q Breakdown of effective field theory (extrapolation invalid)

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

A. Stanford Jan dSE bound on inflation given by past horizon

A. Stanford Jan 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. Stanford Jan

OUTLINE 1.Big Bang & inflation basics 2.Eternal inflation 3.de Sitter Equilibrium cosmology 4.Cosmic curvature from de Sitter Equilibrium cosmology A. Stanford Jan

A. Stanford Jan dSE Cosmology and cosmic curvature The Guth-Farhi process starts inflation with an initial curvature set by the curvature of the FGG Bubble Inflation dilutes the curvature, but dSE cosmology has a minimal amount of inflation

Friedmann Eqn. A. Stanford Jan

A. Stanford Jan Banks & Fischler & Dyson et al. Evolution of curvature radius

A. Stanford Jan Curvature radius set by initial curvature Banks & Fischler & Dyson et al. Evolution of curvature radius

A. Stanford Jan A variety of inflation models, all saturating the dSE bound Curvature radius set by initial curvature Evolution of curvature radius

A. Stanford Jan 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. Stanford Jan AA: arXiv:

A. Stanford Jan 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. Stanford Jan 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. Stanford Jan 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. Stanford Jan 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. Stanford Jan 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. Stanford Jan 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 (plus, no initial conditions problem) Predictions of observable levels of cosmic curvature from dSE cosmology will give an important future test

A. Stanford Jan 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 (plus, no initial conditions problem) Predictions of observable levels of cosmic curvature from dSE cosmology will give an important future test