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Transcript of Les Houches Lectures on Cosmic Inflation Four Parts 1)Introductory material 2)Entropy, Tuning and...
Les Houches Lectures on Cosmic Inflation
Four Parts
1) Introductory material
2) Entropy, Tuning and Equilibrium in Cosmology
3) Classical and quantum probabilities in the multiverse
4) de Sitter equilibrium cosmology
Andreas Albrecht; UC DavisLes Houches Lectures; July-Aug 2013
1Albrecht Les Houches Lectures 2013 Pt. 4
Albrecht Les Houches Lectures 2013 Pt. 4 2
Part 4 Outline
1. de Sitter Equilibrium cosmology
2. Cosmic curvature from de Sitter Equilibrium cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 3
Part 4 Outline
1. de Sitter Equilibrium cosmology
2. Cosmic curvature from de Sitter Equilibrium cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 4
de Sitter Equilibrium (dSE) cosmology
• Take ideas from Holography, to construct a finite cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 5
de Sitter Equilibrium (dSE) cosmology
• Take ideas from Holography, to construct a finite cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 6
de Sitter Equilibrium (dSE) cosmology
• Take ideas from Holography, to construct a finite cosmology
• Build on initial motivation re the appeal of an equilibrium system (no “initial conditions”)
Albrecht Les Houches Lectures 2013 Pt. 4 7
de Sitter Equilibrium (dSE) cosmology
• Take ideas from Holography, to construct a finite cosmology
• Build on initial motivation re the appeal of an equilibrium system (no “initial conditions”)
• Seek the “Bohr Atom” of cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 8
de Sitter Equilibrium (dSE) cosmology
• Take ideas from Holography, to construct a finite cosmology
• Build on initial motivation re the appeal of an equilibrium system (no “initial conditions”)
• Seek the “Bohr Atom” of cosmology• A counterpoint to the infinities of eternal inflation
Albrecht Les Houches Lectures 2013 Pt. 4 9
de Sitter Equilibrium (dSE) cosmology
• Take ideas from Holography, to construct a finite cosmology
• Build on initial motivation re the appeal of an equilibrium system (no “initial conditions”)
• Seek the “Bohr Atom” of cosmology• A counterpoint to the infinities of eternal inflation• Unabashedly exploit uncertainties about the
fundamental physics (i.e. when continuum field theory is good, and when it breaks down) to construct a realistic cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 10
de Sitter Equilibrium (dSE) cosmology
• Take ideas from Holography, to construct a finite cosmology
• Build on initial motivation re the appeal of an equilibrium system (no “initial conditions”)
• Seek the “Bohr Atom” of cosmology• A counterpoint to the infinities of eternal inflation• Unabashedly exploit uncertainties about the
fundamental physics (i.e. when continuum field theory is good, and when it breaks down) to construct a realistic cosmology
AA: arXiv:1104.3315AA: arXiv:0906.1047AA & Sorbo: hep-th/0405270
Albrecht Les Houches Lectures 2013 Pt. 4 11
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Evolution of Cosmic Length
Albrecht Les Houches Lectures 2013 Pt. 4 12
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Evolution of Cosmic Length
Albrecht Les Houches Lectures 2013 Pt. 4 13
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log[
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H0)]
Albrecht Les Houches Lectures 2013 Pt. 4 14
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Albrecht Les Houches Lectures 2013 Pt. 4 15
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domination
Albrecht Les Houches Lectures 2013 Pt. 4 16
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domination
Asymptotic behavior de Sitter Space
Albrecht Les Houches Lectures 2013 Pt. 4 17
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H0)]
The de Sitter horizon
Past horizon of observation event at this time
Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.
Albrecht Les Houches Lectures 2013 Pt. 4 18
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-6
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0
1
2
3
log(a/a0)
log[
(RH/R
H0)]
The de Sitter horizon
Past horizon of observation event at this time
Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.
Albrecht Les Houches Lectures 2013 Pt. 4 19
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-6
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-1
0
1
2
3
log(a/a0)
log[
(RH/R
H0)]
The de Sitter horizon
Past horizon of any observation event deep in the de Sitter era
Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.
Albrecht Les Houches Lectures 2013 Pt. 4 20
-4 -2 0 2 4
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-1
0
1
2
3
log(a/a0)
log[
(RH/R
H0)]
Past horizon of any observation event deep in the de Sitter era
Future horizon of event at reheating (distance photon has traveled, in SBB).Hd
Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.
Albrecht Les Houches Lectures 2013 Pt. 4 21
Implications of the de Sitter horizon
• Maximum entropy
• Gibbons-Hawking Temperature
12
3S A H
8
3GH
GT H
Gibbons & Hawking 1977
Albrecht Les Houches Lectures 2013 Pt. 4 22
2 1S A H
“De Sitter Space: The ultimate equilibrium for the universe?
Horizon
8
3GH
GT H
Albrecht Les Houches Lectures 2013 Pt. 4 23
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
12
3S A H
8
3GH
GT H
SN e
Albrecht Les Houches Lectures 2013 Pt. 4 24
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
12
3S A H
8
3GH
GT H
? SN e
dSE
cosm
olog
y
Albrecht Les Houches Lectures 2013 Pt. 4 25
Equilibrium Cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 26
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
Albrecht Les Houches Lectures 2013 Pt. 4 27
Rare Fluctuation
Albrecht Les Houches Lectures 2013 Pt. 4 28
Rare Fluctuation
Albrecht Les Houches Lectures 2013 Pt. 4 29
Rare Fluctuation
Move Ergodicity to hidden degrees of freedom (we *know* state counting arguments do note apply to the observable universe)AA in prep
Albrecht Les Houches Lectures 2013 Pt. 4 30
Concept:
Realization:
“de Sitter Space”
Albrecht Les Houches Lectures 2013 Pt. 4 31
Rare Fluctuation
Albrecht Les Houches Lectures 2013 Pt. 4 32
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:
s s
GH
m m
T He e
1/2416
3110
0.0013s I II
GeVm cH kg
Albrecht Les Houches Lectures 2013 Pt. 4 33
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:
s s
GH
m m
T He e
1/2416
3110
0.0013s I II
GeVm cH kg
Small seed can produce an entire universe Evade “Boltzmann Brain” problem
Albrecht Les Houches Lectures 2013 Pt. 4 34
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:
s s
GH
m m
T He e
1/2416
3110
0.0013s I II
GeVm cH kg
See also Freivogel et al 2006, Banks 2002
M 0 not a problem for G-F process (A. Ulvestad & AA 2012)
Albrecht Les Houches Lectures 2013 Pt. 4 35
degrees of freedom temporarily break off to form baby universe:
time
Eqm.
Seed Fluctuation
Tunneling
Evolution
Evolution
Evolution
Inflation
Radiation
Matter
de Sitter
IS SN e e
Recombination
Albrecht Les Houches Lectures 2013 Pt. 4 36
degrees of freedom temporarily break off to form baby universe:
time
Eqm.
Seed Fluctuation
Tunneling
Evolution
Evolution
Evolution
Inflation
Radiation
Matter
de Sitter
IS SN e e
Recombination
“Right Timescale”
Albrecht Les Houches Lectures 2013 Pt. 4 37
SN e Implications of finite Hilbert space
• Recurrences
• Eqm.
• Breakdown of continuum field theory
Albrecht Les Houches Lectures 2013 Pt. 4 38
SN e Implications of finite Hilbert space
• Recurrences
• Eqm.
• Breakdown of continuum field theory
Albrecht Les Houches Lectures 2013 Pt. 4 39
SN e Implications of finite Hilbert space
• Recurrences
• Eqm.
• Breakdown of continuum field theory
Albrecht Les Houches Lectures 2013 Pt. 4 40
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)]
I
r
m
This much inflation fills one de Sitter horizon
Albrecht Les Houches Lectures 2013 Pt. 4 41
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This much inflation fills more than one de Sitter horizon, generating total entropyand affecting regions beyond the horizon of the observer
MaxS S
Albrecht Les Houches Lectures 2013 Pt. 4 42
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r
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• In dSE cosmology this region is unphysical.
• Breakdown of effective field theory prevents inflation from filling more than one de Sitter horizon
Albrecht Les Houches Lectures 2013 Pt. 4 43
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r
m
• 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)
Albrecht Les Houches Lectures 2013 Pt. 4 44
-200 -100 0 100 2000
0.5
1
1.5
2
2.5x 10
4
/MP
V/M
GU
T4
To get eternal inflation, we made what we thought was a simple extrapolation, but wound up with a highly problematic theory
Q
Albrecht Les Houches Lectures 2013 Pt. 4 45
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0.5
1
1.5
2
2.5x 10
4
/MP
V/M
GU
T4
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. Q
Breakdown of effective field
theory(extrapolation
invalid)
Albrecht Les Houches Lectures 2013 Pt. 4 46
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:
s s
GH
m m
T He e
1/2416
3110
0.0013s I II
GeVm cH kg
Large exponentially favored saturation of dSE bound
I
Albrecht Les Houches Lectures 2013 Pt. 4 47
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dSE bound on inflation given by past horizon
Albrecht Les Houches Lectures 2013 Pt. 4 48
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dSE bound on inflation given by past horizon
A variety of inflation models, all saturating the dSE bound
Part 4 Outline
1. de Sitter Equilibrium cosmology
2. Cosmic curvature from de Sitter Equilibrium cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 49
Part 4 Outline
1. de Sitter Equilibrium cosmology
2. Cosmic curvature from de Sitter Equilibrium cosmology
Albrecht Les Houches Lectures 2013 Pt. 4 50
Albrecht Les Houches Lectures 2013 Pt. 4 51
Friedmann Eqn.
2
2 8
3 I k r m DE
aH G
a
2a
Albrecht Les Houches Lectures 2013 Pt. 4 52
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Banks & Fischler & Dyson et al.
Evolution of curvature radius 1
k
ca
H
Albrecht Les Houches Lectures 2013 Pt. 4 53
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Curvature radius set by initial curvature
Bk
Banks & Fischler & Dyson et al.
Evolution of curvature radius 1
k
ca
H
Albrecht Les Houches Lectures 2013 Pt. 4 54
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10
log(a/a0)
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A variety of inflation models, all saturating the dSE bound
Curvature radius set by initial curvature
Bk
Evolution of curvature radius 1
k
ca
H
Albrecht Les Houches Lectures 2013 Pt. 4 55
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0
10
log(a/a0)
log[
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)]
A variety of inflation models, all saturating the dSE bound
Curvature radius set by initial curvature
Bk
is given by this gap0
22
0
Hk kk
c k
RH
H R
Evolution of curvature radius 1
k
ca
H
Albrecht Les Houches Lectures 2013 Pt. 4 56
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0
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1.5
2
2.5
log(a/a0)
log[
L/(c
H0-1
)]
AA: arXiv:1104.3315
Albrecht Les Houches Lectures 2013 Pt. 4 57
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
Bk
Albrecht Les Houches Lectures 2013 Pt. 4 58
Image bySurhud 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
k
k
0 /m
Albrecht Les Houches Lectures 2013 Pt. 4 59
Image bySurhud 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
k
k
0 /m
Work in progress on expected values of (Andrew Ulvestad & AA)
Bk
0.5Bk
0.25Bk
0.1Bk
Albrecht Les Houches Lectures 2013 Pt. 4 60
Image bySurhud 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
k
k
0 /m
Work in progress on expected values of (Andrew Ulvestad & AA)
Bk
0.5Bk
0.25Bk
0.1Bk
Albrecht Les Houches Lectures 2013 Pt. 4 61
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-50
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0
10
log(a/a0)
log[
L/(c
H0-1
)]
A variety of inflation models, all saturating the dSE bound
Curvature radius set by initial curvature
Bk
is given by this gap0
22
0
Hk kk
c k
RH
H R
Evolution of curvature radius 1
k
ca
H
Albrecht Les Houches Lectures 2013 Pt. 4 62
Conclusions (Part 4)• 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
Albrecht Les Houches Lectures 2013 Pt. 4 63
Conclusions (Part 4)• 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 (also, alternative to bubble start)
Les Houches Lectures on Cosmic Inflation
Four Parts
1) Introductory material
2) Entropy, Tuning and Equilibrium in Cosmology
3) Classical and quantum probabilities in the multiverse
4) de Sitter equilibrium cosmology
Andreas Albrecht; UC DavisLes Houches Lectures; July-Aug 2013
64Albrecht Les Houches Lectures 2013 Pt. 4
End Part 4
Albrecht Les Houches Lectures 2013 Pt. 4 65
Some parting thoughts
• We are *so* fortunate to be doing cosmology in these times
• Fantastic successes (slow roll inflation & structure)• Great puzzles and challenges (the Guth dream, dark
energy)• Which ideas to import from everyday physics, which to
throw out?• Which ideas are too radical, which not radical enough?• Let us all make the most of these amazing
opportunities, and navigate these difficult issues as bravely and energetically as possible!