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