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Stabilization of Moduli in String Theory I , II TowardsTowards StringString Cosmology.Cosmology. StabilizationStabilization ofof modulimoduli inin stringstring theorytheory II ,, IIII RenataRenata KalloshKallosh Stanford Fields Institute, Toronto, May 9, 10,11 2005 I. Towards String Cosmology In this pedagogical lecture some basic part of the standard cosmological model which is most relevant for the fundamental theoretical physics will be explained. The common features and differences between early universe inflation and late-time acceleration will be stressed. Some recent attempts to address the issues of cosmology in string theory and higher dimensional supergravity with the emphasis on successes and still unsolved problems will be presented. OutlineOutline ofof LectureLecture II 1. Cosmological Concordance Model and Problems of M/String Theory in Explaining the Observations. 2. Flux Compactification and Stabilization of Moduli, Metastable de Sitter Space in String Theory 3. Ghost-Free de Sitter Supergravities as Consistent Reductions of String and M-theory: collapsing universe 4. Landscape of String Theory, Statistics 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 astrophysics 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 dark energy that’s also true.” -- Edward Witten WhatWhat isis soso embarrassingembarrassing aboutabout it?it? TwoTwo generalgeneral problems:problems: • Why is the cosmological constant so small, in Planck density units ? • Why ? Coincidence problem. addressed by anthropic principle, 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 gravity • Beyond standard model particle physics • Supersymmetry, supergravity: d=10/d=11 maximal dimension, 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, SPLIT SUPERSYMMETRY IFIF SUSYSUSY ISIS THERETHERE The significance of discovery of supersymmetry in nature, (which will manifests itself via existence of supersymmetric particles) 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 → Field 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 dilaton 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 axion-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 Conifold The throat geometry 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 Minkowski space! KahlerKahler modulimoduli problemproblem (in(in particular,particular, overalloverall volume)volume) KKLT proposal i) non-perturbative superpotential from Euclidean D3-branes 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 lead to AdS space (negative vacuum energy) with unbroken SUSY and stabilized volume Uplifting AdS space to a metastable dS space (positive vacuum energy) by adding anti-D3 brane (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.
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