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Home , Moduli (physics), Renata Kallosh, String (physics), String cosmology, String theory, String theory landscape

TowardsTowards StringString .Cosmology. StabilizationStabilization ofof modulimoduli inin stringstring theorytheory II ,, IIII

RenataRenata KalloshKallosh Stanford

Fields Institute, Toronto, May 9, 10,11 2005 I. Towards Cosmology

„ In this pedagogical lecture some basic part of the standard cosmological model which is most relevant for the fundamental theoretical will be explained. The common features and differences between early and late-time acceleration will be stressed. Some recent attempts to address the issues of cosmology in string and higher dimensional with the emphasis on successes and still unsolved problems will be presented. OutlineOutline ofof LectureLecture II 1. Cosmological Concordance Model and Problems of M/ in Explaining the Observations.

2. Flux Compactification and Stabilization of , Metastable de Sitter Space in String Theory

3. -Free de Sitter Supergravities as Consistent Reductions of String and M-theory: collapsing universe

4. Landscape of String Theory, of Flux Vacua, CC problem

5. Inflation in String Theory, Cosmic Strings, Scale of SUSY breaking Our Universe is an Ultimate Test of Fundamental Physics

„ High-energy accelerators will probe the scale of energies way below GUT scales

„ Cosmology and are sources of data in the gravitational sector of the fundamental physics (above GUT, near Planck scale) InIn viewview ofof thethe recentrecent cosmologicalcosmological observationsobservations supportingsupporting darkdark energyenergy andand inflationinflation itit isis fairfair toto saysay thatthat wewe dodo notnot reallyreally knowknow whatwhat isis ““fundamentalfundamental physicsphysics””

“ Most embarrassing observation in physics – that’s the only quick thing I can say about that’s also true.” -- WhatWhat isis soso embarrassingembarrassing aboutabout it?it?

TwoTwo generalgeneral problems:problems: • Why is the so small, in Planck density units ?

• Why ? Coincidence problem.

addressed by , Weinberg 1987 TheThe thirdthird problem:problem:

Two years ago it was not clear how one could possibly incorporate a positive cosmological constant in string theory This was the main reason of embarrassment for string theorists, because of the cosmological data suggesting that

addressed by KKLT, 2003 OneOne cancan argueargue thatthat M/StringM/String theorytheory isis fundamentalfundamental

• Perturbative finiteness of quantum • Beyond physics • , supergravity: d=10/d=11 maximal , almost unique • TheThe bestbest theorytheory wewe havehave nownow (unless it can be ruled out by observations) ™ Stringy Cloak for a Null Singularity Higgs, Standard Model Supersymmetry,

IFIF SUSYSUSY ISIS THERETHERE The significance of discovery of supersymmetry in nature, (which will manifests itself via existence of supersymmetric ) is the discovery of the fermionicfermionic dimensionsdimensions ofof spacetimespacetime. ItIt willwill bebe thethe mostmost fundamentalfundamental discoverydiscovery inin physicsphysics afterafter EinsteinEinstein’’ss relativityrelativity

SUPERSYMMETRY

Gravity Supergravity/String theory Fundamental Physics Astrophysics → Cosmology → Theory a(t) → Equation of state w(z) → V(φ) SN CMB V ( φ( a(t) ) ) LSS

The subtle slowing and growth of scales with time STScI – a(t) –map out the cosmic history like tree rings map out the Earth’s climate history.

Map the expansion history of the universe Discovery!Discovery! AccelerationAcceleration

Exploding stars – supernovae – are bright beacons that allow us to measure precisely the expansion over the last 10 billion years. WMAPWMAP andand thethe temperaturetemperature ofof thethe skysky

WMAPWMAP andand spectrumspectrum ofof thethe microwavemicrowave backgroundbackground anisotropyanisotropy Cmbgg OmOl How much dark energy is there?

Closed

Open How much dark energy is there? closed Cmbggflat OmOl CMB open How much dark energy is there? closed Cmbggflat OmOl CMB open +

LSS

WMAP + SDSS: lots How much dark energy is there? closed Cmbggflat OmOl CMB open +

LSS How much dark energy is there? closed Cmbggflat OmOl CMB open +

LSS DARKDARK ENERGYENERGY

Total energy in 3d flat FRW universe O

70% of the total energy of the universe is DARKDARK astro-ph/0407372

Spring 2005

NewNew datadata

Boomerang,…, WMAP, 2005 ??? Planck, SNAP, LSST ..., 2010-2012

ItIt isis likelylikely thatthat 70%70% ofof DarkDark EnergyEnergy andand EarlyEarly UniverseUniverse InflationInflation willwill bebe confirmed,confirmed, butbut wewe havehave toto waitwait CosmologicalCosmological ConcordanceConcordance ModelModel

„ Early Universe Inflation „ Current Acceleration „ NearNear dede SitterSitter spacespace „ NearNear dede SitterSitter spacespace „ 13.7 billion years ago „ Now „ During 10^{-35} sec „ During few billion years StringString TheoryTheory andand CosmologyCosmology

All observations so far seem to fit 4d Einstein GR. We need to know how to get this picture from the compactified 10d string theory or 11d M-theory and supergravity

HowHow toto getget dede SitterSitter oror nearnear dede SitterSitter 4d4d space?space? ADS/CFTADS/CFT CORRESPONDENCECORRESPONDENCE

„ A major activity of string community from 1997 is AdS/CFT

„ ??? NoNo--GoGo TheoremsTheorems forfor 4d4d dede SitterSitter SpaceSpace fromfrom 10/11d10/11d string/Mstring/M theorytheory

• Gibbons 19851985 • de Wit, Smit, Hari Dass, 19871987 • Maldacena, Nunez, 20012001

HowHow toto gogo aroundaround thethe conditionsconditions forfor dede SitterSitter nono--gogo theorems?theorems? HowHow toto performperform aa compactificationcompactification fromfrom 10/1110/11 dimensionsdimensions toto 44 dimensionsdimensions andand stabilizestabilize thethe moduli?moduli? SpaceSpace ofof M/StringM/String TheoryTheory vacuavacua

New developments

• It was known for 20 years that string theory is not easily compatible with cosmology • During the last few years this became a very serious issue RecentRecent proposalproposal

TowardsTowards cosmologycosmology inin typetype IIBIIB stringstring theorytheory

Dilaton stabilization Giddings, Kachru and Polchinski 2001

Volume stabilization, KKLT Kachru, R. K, Linde, Trivedi 2003

Kachru, R. K., Maldacena, McAllister, Linde, Trivedi 2003 AAA photographicphotographicphotographic imageimageimage ofofof quantumquantumquantum fluctuationsfluctuationsfluctuations blownblownblown upupup tototo thethethe sizesizesize ofofof thethethe universeuniverseuniverse InflationaryInflationary slowslow rollroll parametersparameters inin unitsunits

Primordial slope

Derivatives w. r. to canonicaly normalized fields!

Observational data CanCan StringString TheoryTheory AffordAfford thethe RunawayRunaway Moduli?Moduli? CompareCompare withwith observationsobservations

1. ForFor earlyearly universeuniverse inflationinflation 2. ForFor darkdark energyenergy For the For the total volume

BothBoth stringystringy modulimoduli havehave veryvery steepsteep potentialspotentials incompatibleincompatible withwith thethe datadata eveneven forfor thethe currentcurrent accelerationacceleration ofof thethe universe,universe, particularlyparticularly thethe totaltotal volumevolume FLUXFLUX COMPACTIFICATION,COMPACTIFICATION, IIBIIB STRINGSTRING

„ Non-perturbative string theory, perturbative d=10 supergravity

Leads to stabilization of -dilaton and complex structure moduli

KahlerKahler modulimoduli stabilizationstabilization cannotcannot bebe achievedachieved viavia fluxflux compactificationcompactification FluxFlux compactificationcompactification andand modulimoduli stabilizationstabilization inin IIBIIB stringstring theorytheory (supergravity(supergravity ++ locallocal sources)sources) The

TheThe fluxesfluxes fixfix thethe shapeshape ofof CalabiCalabi--YauYau andand thethe dilatondilaton--axionaxion Wa KK andand MM areare integerinteger fluxesfluxes associatedassociated withwith thethe 33--formsforms inin typeIIBtypeIIB theorytheory Deformed

The throat has a highly warped region NoNo--scalescale PotentialPotential isis PositivePositive-- DefiniteDefinite NoNo--scalescale

Runaway potential for the volume moduli. Dilaton and shape moduli are generically fixed in ! KahlerKahler modulimoduli problemproblem (in(in particular,particular, overalloverall volume)volume) KKLT proposal i) non-perturbative superpotential from Euclidean D3- wrapped on special 4-cycles ii) non-perturbative superpotential from pure SYM on a stack of D7’s on EffectiveEffective theorytheory forfor thethe volumevolume modulimoduli

SolveSolve

the volume is stabilized in AdSAdS critical point in the regime of validity of calculations!

AdS minimum VolumeVolume stabilizationstabilization BasicBasic steps:steps:

Warped geometry of the compactified space and nonperturbative effects to AdS space (negative energy) with unbroken SUSY and stabilized volume

Uplifting AdS space to a metastable dS space (positive ) by adding anti-D3 (or D7 brane with fluxes)

AdS minimum Metastable dS minimum KKLTKKLT basedbased newnew ideasideas

LandscapeLandscape Susskind Statistics of FluxFlux VacuaVacua Douglas

ModelsModels ofof InflationInflation inin StringString TheoryTheory

Cosmic Strings Produced by the end of Inflation, OBSERVABLE IN THE FUTURE?

Copeland, Myers, Polchinski CMB power spectrum

WMAP data

strings

Acoustic peaks come from temporal coherence. Inflation has it, strings don’t. String contribution < 10% implies Gμ ~< 10−6. LIGO/LISALIGO/LISA signalssignals fromfrom stringstring cuspscusps

h LIGO I Cosmic strings could be the brightest GW Advanced sources, over a wide LIGO cusps kinks range of Gμ pulsar bound

α ~ 50Gμ Damour and Vilenkin 2001 h

cusps s nk ki Field theory strings?

LISA String theory strings? AA generalgeneral ProblemProblem ofof DarkDark Energy:Energy: slow roll conditions

Dark energy can be observationally different from the cosmological constant only if an additional coincidence problem is resolved. In the language of the effective scalar theory, one should require thatthe slope of the potential is anomalously small,

To distinguish dark energy from the cosmological constant, the slope must be of the same as the cosmological constant:

This would be a coincidence (additional fine-tuning), which does not have any motivation (even anthropic) in most of the dark energy models. An exception from this rule is provided by Ghost-Free de Sitter supergravities, consistent reductions from M/String Theory DeDe SitterSitter GaugedGauged SupergravitiesSupergravities as a consistent Pauli reduction of M/String theory on hyperbolic spaces

11/10 d supergravities lead to ghost-free gauged 4d supergravities with extended supersymmetry dS always correspond to saddle points

R. K., Linde, Prokushkin, Shmakova, 2002 Cvetic, Gibbons, Pope, 2004 Acharya, Denef, Valandro, 2005

Toy models of dark energy with w > - 1, with future collapse and anthropic explanation of the scale of CC

Dark energy slow-roll conditions are satisfied authomatically

TypicalTypical AdSAdS extremaextrema,, maximummaximum andand saddlesaddle pointspoints LIFETIMELIFETIME ™ KKLT model starts with an AdS minimum due to non-perturbative effects. It can be uplifted to dS minimum with the barrier protecting it from the decay. This dS is metastable, practically CC t ~ 1010120 ™ Exact solutions of 11d M/string-supergravity with fluxes: ghost-free dS supergravities. Unstable since dS is a saddle point. Prediction R. K., Linde t ~ 1010 -1011 Bousso, Polchinski; Vilenkin, Linde Landscape Idea Landscape Idea Susskind; Douglas KKLT

• With account of loop corrections each vacuum will change. However, the total lanscape picture with many vacua will survive • There are many vacua with negative, vanishing and positive energies • Somewhere there is our vacuum with

where N, the number of vacua, is required to be

The number of phenomenologically (or anthropically) acceptable vacua is smaller than the number of total vacua

IsIs therethere aa betterbetter idea?idea? StringString TheoryTheory LandscapeLandscape

100 1000 PerhapsPerhaps 1010100 -10-101000 Inflationary differentdifferent vacuavacua slow-roll valleys With KKLT and other versions of dS we have found that vacua with positive CC are possible in string theory and equation of state with

is consistent with string theory. To explain any other equation of state of dark energy, like

remains extremely difficult

and, particularly, does not seem possible in consistent string theory.

Modified gravity and other ideas (some do not seem to be consistent with SUSY) TwoTwo typestypes ofof stringstring inflationinflation models:models:

„ Brane inflation (Dvali-Tye) The field corresponds to the between branes in Calabi-Yau space. KKLMMT and D3/D7

„ Modular Inflation. TheThe simplestsimplest classclass ofof models.models. OnlyOnly modulimoduli thatthat areare alreadyalready presentpresent inin thethe KKLTKKLT model.model. RacetrackRacetrack InflationInflation NewNew :: inflationaryinflationary modelsmodels inin stringstring theorytheory

KKLMMT brane-anti-brane inflation

D3/D7 brane inflation

D-term Dasgupta, Herdeiro, inflation Hirano, R.K.

Racetrack modular inflation Blanco-Pilado, Burgess, Cline, Escoda, Gomes-Reino, Kallosh, Linde, Quevedo

DBI inflation, Silverstein et al Important New Results and Consequences of the New Picture 2004-2005 „ Denef, Douglas, Florea, Grassi, Kachru : examples of all moduli stabilization „ New models with all moduli fixed: Aspinwall, Bergshoeff, R. K. Kashani-Poor, Sorokin,Tomasiello „ Scale of susy breaking: if we have to fine- tune CC we may need to fine-tune the Higgs , the generic low scale susy may be not valid. Split supersymmetry Arkani-Hamed, Dimopoulos Major problem:

New mechanisms of volume stabilization A Simple Example of Moduli Fixing

Aspinwall, R.K. We analyze M-theory compactified on K3xK3 with fluxes and its F-theory limit, which is dual to an of the type IIB string on

WeWe argueargue thatthat instantoninstanton effectseffects willwill genericallygenerically fixfix allall ofof thethe moduli.moduli.

ModuliModuli spacespace isis nono moremore SummarySummary onon StringString CosmologyCosmology

„ OverOver thethe lastlast fewfew yearsyears wewe werewere ableable toto constructconstruct thethe firstfirst modelmodel ofof thethe cosmologicalcosmological constant/darkconstant/dark energyenergy inin thethe contextcontext ofof stringstring theorytheory

„ SeveralSeveral modelsmodels ofof stringstring theorytheory inflationinflation areare availableavailable now,now, muchmuch moremore workwork isis requiredrequired

„ FutureFuture cosmologicalcosmological andand particleparticle physicsphysics datadata willwill helphelp usus toto testtest thethe newnew ideasideas inin stringstring theorytheory andand cosmologycosmology PLANCK

SNAP

LHC SNAP