Cosmology and String Cosmology and String TheoryTheory
F. Quevedo CambridgeCORFU 2005
OUTLINEOUTLINE
String Cosmology before 2003String Cosmology before 2003
The KKLT Scenario and the String The KKLT Scenario and the String LandscapeLandscape
Inflation and Moduli StabilizationInflation and Moduli Stabilization
FQ hepth/0210292FQ hepth/0210292
STRING COSMOLOGYSTRING COSMOLOGY
String theory is fundamental then it should String theory is fundamental then it should have important implications in early have important implications in early universeuniverse
Quantum gravity Big bang or beforeQuantum gravity Big bang or before
Experimental tests of the theory?Experimental tests of the theory?
OBSERVATIONAL OBSERVATIONAL CHALLENGESCHALLENGES
CMB AnisotropiesCMB Anisotropies
EXPERIMENTALEXPERIMENTAL
EVIDENCE FOR EVIDENCE FOR ΛΛ>0>0
Ω = ΩΛ + ΩM + ΩK = 1
Ω = ρ/ρc relative energy density
K = -1,0,1 open, flat, closed universe
ΩΛ ~ 0.7, ΩM~ 0.3, Ωk~ 0
PROBLEMPROBLEM
Do not understand the theory in Do not understand the theory in time dependent backgrounds !!!time dependent backgrounds !!!
Effective Field TheoriesEffective Field Theories
General AspectsGeneral Aspects
Branderberger-Vafa Scenario ((SBranderberger-Vafa Scenario ((S11))99 x time) x time)
T-dualityT-duality
Minimal distance !Minimal distance !
Winding modes D=4 (since 2+2=4)!Winding modes D=4 (since 2+2=4)!
Pre Big-Bang CosmologyPre Big-Bang Cosmology Gasperini, Veneziano,…Gasperini, Veneziano,…
t=0 singularity + strong coupling
String Theory and 4D String Theory and 4D InflationInflation
MOTIVATIONMOTIVATION
Inflation: very successful but only Inflation: very successful but only scenarios in search of a theoryscenarios in search of a theory
String theory: fundamental theory but String theory: fundamental theory but lacks experimental tests.lacks experimental tests.
Is it possible to `derive’ inflation from string Is it possible to `derive’ inflation from string theory?theory?
Need to compute scalar potential from String Need to compute scalar potential from String theory satisfying slow-roll conditions:theory satisfying slow-roll conditions:
Number of e-folds N>60
Density perturbations
HISTORYHISTORYt<1986 Calabi-Yau String Compactifications: Many free moduli (size t<1986 Calabi-Yau String Compactifications: Many free moduli (size and shape of extra dimensions) from gand shape of extra dimensions) from gmnmn, B, Bmnmn, , φφ, A, Amm
II
1986<t<1991 Geometric moduli: candidate for inflaton fields. But no 1986<t<1991 Geometric moduli: candidate for inflaton fields. But no potentials (potentials (V=0).V=0).
Or V too steep:Or V too steep:
Dilaton S, Kähler TComplex structure UWilson lines W
Candelas et al.Candelas et al.
Binetruy-Gaillard, Banks et alBinetruy-Gaillard, Banks et al
Brustein-SteinhardtBrustein-Steinhardt
New Problems:New Problems:
OvershootingOvershooting(natural to end up in runaway)(natural to end up in runaway)
Cosmological Moduli ProblemCosmological Moduli Problem
(moduli overclose the universe or ruin (moduli overclose the universe or ruin nucleosynthesis)nucleosynthesis)
Brustein-SteinhardtBrustein-Steinhardt
Coughlan et al.Coughlan et al.
Banks et al.Banks et al.
De Carlos et al.De Carlos et al.
t=1995-1998t=1995-1998 The Brane WorldThe Brane WorldADD, Horava-Witten,…
t=1998 More moduli! : D-brane inflation. But V=0 or non-calculable.t=1998 More moduli! : D-brane inflation. But V=0 or non-calculable.
t=2001 Brane/Antibrane inflation:t=2001 Brane/Antibrane inflation:
Dvali-Tye
Generically no slow roll,
but…
Burgess et al., Dvali et al
VV
YYtachyontachyon
Tachyon complex topological defects Tachyon complex topological defects D (p-2) branes cosmic strings !D (p-2) branes cosmic strings !
End of inflation: Open string tachyonEnd of inflation: Open string tachyonBurgess Burgess
et al.et al.
Tye et al. Tye et al.
Copeland et al.Copeland et al.
Sen, Burgess Sen, Burgess et al.et al.
Intersecting Brane Inflation
Y: Inflaton
End of inflation: tachyon
Also: D3-D7 inflation
Garcia-Bellido et al.Garcia-Bellido et al.
Kallosh et al.Kallosh et al.
Ekpyrotic/Cyclic ScenarioEkpyrotic/Cyclic Scenario
a(0)=0 weak coupling (bounce?)
But: singularity? Potential by hand,…
Horava Witten 11D
Outstanding ProblemOutstanding Problem
Moduli StabilizationModuli Stabilization
A Solution: turn-on fluxes
t> 2003 KKLT Scenario
……GKP, KKLT, …GKP, KKLT, …
KKLT ScenarioKKLT Scenario
Type IIB String on Calabi-Yau orientifoldType IIB String on Calabi-Yau orientifold
Turn on FluxesTurn on Fluxes ∫∫aa FF33 = n = n aa ∫ ∫bb HH33 = m = m bb
SuperpotentialSuperpotential W =W = ∫ ∫ GG33 ΛΛ ΩΩ, G, G3 3 = = FF3 3 –iS–iS HH33
Scalar Potential:Scalar Potential: V= e V= eKK |D |DaaW|W|22 MinimumMinimum D DaaW = 0 W = 0 Fixes UFixes Uaa and S and S T moduli unfixed: T moduli unfixed: No-Scale modelsNo-Scale models
Size of cycle a = USize of cycle a = Uaa
GKPGKP
……GKP, KKLT, …GKP, KKLT, …
4D Compactifications4D Compactifications
To fix KTo fix Kähler moduli: Non-perturbative D7 effectsähler moduli: Non-perturbative D7 effects
FluxesFluxes Non-perturbativeNon-perturbative
VolumeVolume
SUSY AdS minimumSUSY AdS minimum
(W(W00 << 1) << 1)
Lifting to de Sitter (add anti D3 branes, D-terms, etc.)Lifting to de Sitter (add anti D3 branes, D-terms, etc.)
SUSY breaking termSUSY breaking term
KKLT, BKQ, SSKKLT, BKQ, SS
VV
axionaxion volumevolume
The LandscapeThe Landscape
Huge number of discrete Huge number of discrete vacua >10vacua >10500500
StatisticsStatistics
Randall-Sundrum Randall-Sundrum warping from strings!warping from strings!
Non SUSY de SitterNon SUSY de Sitter
Dark energy?Dark energy?
`SM’ on D3/D7branes`SM’ on D3/D7branes
Soft SUSY breaking?Soft SUSY breaking?
Inflation?Inflation?
AD, DD, DDF, GKTT,CQ,BGHLWAD, DD, DDF, GKTT,CQ,BGHLW
GKPGKP
BPBP
CG-MQUCG-MQU
Populating the LandscapePopulating the Landscape
Classical Solutions
Quantum decay(tunnel efect)
Multiverse and Eternal InflationMultiverse and Eternal Inflation
Realistic ModelsRealistic ModelsCG-MQU, CSUCG-MQU, CSU
Exponentially Large VolumesExponentially Large Volumes
At least two KAt least two Kähler moduli (hähler moduli (h2121>h>h1111>1)>1)
Perturbative corrections to KPerturbative corrections to K
Example :Example :
Exponentially large !Exponentially large !
BBCQ, CQSBBCQ, CQS
Non SUSY AdSNon SUSY AdS
WW00~1-10~1-10
String scale: MsString scale: Ms22=Mp=Mp22//VV
KKLT AdSKKLT AdS
Non SUSY AdSNon SUSY AdS
WW00~10~10-10-10
WW00<10<10-11-11
Both minima Both minima mergemerge
Inflation and Moduli Inflation and Moduli StabilizationStabilization
D3 BraneD3 Brane
φφ
φφ inflaton field inflaton field
Brane-Antibrane InflationBrane-Antibrane Inflation
KKLMMT, HKP, KTW, KKLMMT, HKP, KTW, FT, BCSQ, …FT, BCSQ, …
Slow-roll (large field) inflation possible.Slow-roll (large field) inflation possible.
Need 1/1000 fine tuning of parameters to Need 1/1000 fine tuning of parameters to
get 60-efoldings (get 60-efoldings (ηη-problem)-problem)
NN~60, ~60, δδHH~10~10-5-5 for for
Ms~ 10Ms~ 101515 GeV GeV
nnss~1.05~1.05 Burgess, Cline, Burgess, Cline, Stoica, FQStoica, FQ
Needs at least two throats !
Also: D3-D7 on K3xT2
DBI in the sky
Kallosh et al.Kallosh et al.
Silverstein-Tong, ChenSilverstein-Tong, Chen
Warped Tachyonic InflationWarped Tachyonic Inflation
A,B depend on warping (fluxes) and E&M fields on non-A,B depend on warping (fluxes) and E&M fields on non-BPS brane. If A,BBPS brane. If A,B~1 no slow-roll~1 no slow-roll
AB large slow-rollAB large slow-roll
No fine-tuning! But need large fluxesNo fine-tuning! But need large fluxes
Sen, Raeymakers, Cremades-Sinha-FQSen, Raeymakers, Cremades-Sinha-FQ
INITIAL CONDITIONSINITIAL CONDITIONS
Sen’s open string Sen’s open string completeness completeness conjectureconjecture
t -tt -t
Pre big-bang ! ?Pre big-bang ! ?
Inflation and compactification or big-crunch/bangInflation and compactification or big-crunch/bang
and decompactification ! ?and decompactification ! ?
Racetrack InflationRacetrack Inflation
Topological eternal inflation !Topological eternal inflation !
Slow roll if 1/1000 fine tuning, Slow roll if 1/1000 fine tuning,
NN~60, ~60, δδHH~10~10-5 -5 for Ms~10for Ms~1015 15 GeVGeV
nnss ~ 0.95~ 0.95
Blanco-Pillado et al.Blanco-Pillado et al.
Improved RacetrackImproved Racetrack Blanco-Pillado et al.Blanco-Pillado et al.
Douglas et al.Douglas et al.
Explicitly derived model
Similar physics
KKähler Moduli Inflationähler Moduli Inflation
Any Calabi-Yau:
h2121>>h1111>2
volume τn
V
Conlon-FQConlon-FQ
Large field inflation
No fine-tuning!!
0.960<n<0.967
CONCLUSIONSCONCLUSIONS
Exciting timesExciting timesType IIB: Several inflationary scenarios, Type IIB: Several inflationary scenarios,
Inflaton: Kahler modulus, brane sparation, tachyon, Wilson lines , Inflaton: Kahler modulus, brane sparation, tachyon, Wilson lines , Complex structure moduli (?).Complex structure moduli (?).
ReheatingReheatingExtensions to other string theories (Extensions to other string theories (Becker et alBecker et al))Initial conditionsInitial conditionsOvershooting problem,….Overshooting problem,….
Open questions