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Cosmology and String Theory. F. Quevedo Cambridge CORFU 2005. OUTLINE. String Cosmology before 2003 The KKLT Scenario and the String Landscape Inflation and Moduli Stabilization. FQ hepth/0210292. STRING COSMOLOGY.
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Cosmology and String Theory F. Quevedo Cambridge CORFU 2005
OUTLINE • String Cosmology before 2003 • The KKLT Scenario and the String Landscape • Inflation and Moduli Stabilization FQ hepth/0210292
STRING COSMOLOGY • String theory is fundamental then it should have important implications in early universe • Quantum gravity Big bang or before • Experimental tests of the theory?
EXPERIMENTALEVIDENCE FOR Λ>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
PROBLEM Do not understand the theory in time dependent backgrounds !!!
General Aspects • Branderberger-Vafa Scenario ((S1)9 x time) T-duality Minimal distance ! Winding modes D=4 (since 2+2=4)!
Gasperini, Veneziano,… • Pre Big-Bang Cosmology t=0 singularity + strong coupling
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?
Need to compute scalar potential from String theory satisfying slow-roll conditions: Number of e-folds N>60 Density perturbations
HISTORY • t<1986 Calabi-Yau String Compactifications: Many free moduli (size and shape of extra dimensions) from gmn, Bmn, φ, AmI • 1986<t<1991 Geometric moduli: candidate for inflaton fields. But no potentials (V=0). Or V too steep: Candelas et al. Dilaton S, Kähler T Complex structure U Wilson lines W Binetruy-Gaillard, Banks et al Brustein-Steinhardt
New Problems: Overshooting (natural to end up in runaway) Cosmological Moduli Problem (moduli overclose the universe or ruin nucleosynthesis) Brustein-Steinhardt Coughlan et al. Banks et al. De Carlos et al.
t=1995-1998The Brane World ADD, Horava-Witten,…
t=1998 More moduli! : D-brane inflation. But V=0 or non-calculable. t=2001 Brane/Antibrane inflation: Dvali-Tye Burgess et al., Dvali et al Generically no slow roll, but…
End of inflation: Open string tachyon Burgess et al. V tachyon Y Tachyon complex topological defects D (p-2) branes cosmic strings ! Sen, Burgess et al. Tye et al. Copeland et al.
Intersecting Brane Inflation Garcia-Bellido et al. Y: Inflaton End of inflation: tachyon Also: D3-D7 inflation Kallosh et al.
Ekpyrotic/Cyclic Scenario Horava Witten 11D a(0)=0 weak coupling (bounce?) But: singularity? Potential by hand,…
Outstanding Problem • Moduli Stabilization A Solution: turn-on fluxes t> 2003 KKLT Scenario …GKP, KKLT, …
The Problem • String/M-Theory unique but has many solutions or vacua. • Some solutions resemble the Standard Model and MSSM. • Degeneracy : Discrete + Continuous (SUSY) . • Outstanding Problems: SUSY breaking + Vacuum degeneracy.
History • t<1986 Calabi-Yau String Compactifications: Many free moduli (size and shape of extra dimensions) • 1986<t<1991 Gaugino condensation and T-duality • 1991<t<2002 More moduli! (D-brane positions) • t>2002 GKP/ KKLT : Fluxes fix moduli Dilaton S, Kähler T Complex structure U CHSW Fix S and one T DIN, DRSW, K, FILQ, FMTV …GKP, KKLT, …
KKLT Scenario …GKP, KKLT, … • Type IIB String on Calabi-Yau orientifold • Turn on Fluxes ∫aF3 = n a ∫bH3 = m b SuperpotentialW = ∫ G3ΛΩ, G3 = F3 –iSH3 Scalar Potential: V= eK |DaW|2 Minimum DaW = 0 Fixes Ua and S T moduli unfixed: No-Scale models Size of cycle a = Ua GKP
To fix Kähler moduli: Non-perturbative D7 effects Non-perturbative Fluxes Volume SUSY AdS minimum (W0 << 1)
Multi-throat compactification
Lifting to de Sitter (add anti D3 branes, D-terms, etc.) KKLT, BKQ, SS, VZ SUSY breaking term V axion volume
The Landscape • Huge number of discrete vacua >10500 • Statistics • Randall-Sundrum warping from strings! • Non SUSY de Sitter • Dark energy? • `SM’ on D3/D7branes • Soft SUSY breaking? • Inflation? AD, DD, DDF, GKTT,CQ,BGHLW GKP BP CG-MQU
Populating the Landscape Classical Solutions Quantum decay (tunnel efect)
Realistic Models CG-MQU, CSU
Exponentially Large Volumes BBCQ, CQS • At least two Kähler moduli (h21>h11>1) • Perturbative corrections to K Example : Exponentially large !
Non SUSY AdS W0~1-10 String scale: Ms2=Mp2/V
KKLT AdS Non SUSY AdS Both minima merge W0~10-10 W0<10-11
Soft SUSY Breaking • From KKLT not explicit model but interesting general behaviour (D/F term breaking, AMSB, …) • From lifting of large volume models CFNOP,CJO CQS Matter on D3 Ms~1013 GeV Gaugino masses ~ 102 GeV, scalars m ~107 GeV Ms=MGUT viable if warping, Ms=Tev `viable’ if SM anti D-brane (but 5th force and cmp?)
Brane-Antibrane Inflation KKLMMT, HKP, KTW, FT, BCSQ, … φ inflaton field D3 Brane φ
Slow-roll (large field) inflation possible. Need 1/1000 fine tuning of parameters to get 60-efoldings (η-problem) N~60, δH~10-5 for Ms~ 1015 GeV ns~1.05 Burgess, Cline, Stoica, FQ Needs at least two throats ! Kallosh et al. Also: D3-D7 on K3xT2 DBI in the sky Silverstein-Tong, Chen
Warped Tachyonic Inflation Sen, Raeymakers, Cremades-Sinha-FQ A,B depend on warping (fluxes) and E&M fields on non-BPS brane. If A,B~1 no slow-roll AB large slow-roll No fine-tuning! But need large fluxes
INITIAL CONDITIONS Sen’s open string completeness conjecture t -t Pre big-bang ! ? Inflation and compactification or big-crunch/bang and decompactification ! ?
Racetrack Inflation Blanco-Pillado et al. Topological eternal inflation ! Slow roll if 1/1000 fine tuning, N~60, δH~10-5 for Ms~1015 GeV ns~ 0.95 Also for W0=0 if add matter Lalak, Ross, Sarkar
Improved Racetrack Blanco-Pillado et al. Douglas et al. Explicitly derived model Similar physics
Kähler Moduli Inflation Conlon-FQ Any Calabi-Yau: h21>h11>2 V Large field inflation No fine-tuning!! 0.960<n<0.967 τn volume
CONCLUSIONS • Exciting times • Type IIB: Several inflationary scenarios, Inflaton: Kahler modulus, brane sparation, tachyon, Wilson lines , Complex structure moduli (?). • Reheating • Extensions to other string theories (Becker et al) • Initial conditions • Overshooting problem,…. OPEN QUESTIONS