inflationary scenarios from string theory
DESCRIPTION
Inflationary Scenarios from String Theory. F. Quevedo Cambridge COSMO 2005. MOTIVATION. Inflation: very successful but only scenarios in search of a theory String theory: fundamental theory but lacks experimental tests. Is it possible to `derive’ inflation from string theory?. HISTORY. - PowerPoint PPT PresentationTRANSCRIPT
Inflationary Scenarios from Inflationary Scenarios from String TheoryString Theory
F. Quevedo CambridgeCOSMO 2005
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?
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
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.
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, …
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
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