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