1. Moduli Stabilization: A Revolution in String Phenomenology / Cosmology ? F. Quevedo SUSY 2005

2. The Problem String/M-Theory unique but has many solutions or vacua. 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.

3. 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 Fix S and one T CHSW DIN, DRSW, K, FILQ, FMTV …GKP, KKLT, …

4. KKLT Scenario Type IIB String on Calabi-Yau orientifold Type IIB String on Calabi-Yau orientifold Turn on Fluxes ∫ a F 3 = n a ∫ b H 3 = m b ∫ a F 3 = n a ∫ b H 3 = m b Superpotential W = ∫ G 3 Λ Ω, G 3 = F 3 –iS H 3 Superpotential W = ∫ G 3 Λ Ω, G 3 = F 3 –iS H 3 Scalar Potential: V= e K |D a W| 2 Scalar Potential: V= e K |D a W| 2 Minimum D a W = 0 Fixes U a and S Minimum D a W = 0 Fixes U a and S T moduli unfixed: No-Scale models T moduli unfixed: No-Scale models Size of cycle a = U a GKP

5. To fix Kähler moduli: Non-perturbative D7 effects Fluxes Non-perturbative Volume SUSY AdS minimum (W 0 << 1)

6. Lifting to de Sitter (add anti D3 branes, D-terms, etc.) SUSY breaking term KKLT, BKQ, SS V axionvolume

7. The Landscape Huge number of discrete vacua >10 500 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

8. Realistic Models CG-MQU, CSU

9. Exponentially Large Volumes At least two Kähler moduli (h 21 >h 11 >1) Perturbative corrections to K Example : Exponentially large ! BBCQ, CQS

10. Non SUSY AdS W 0 ~1-10 String scale: Ms 2 =Mp 2 /V

11. KKLT AdS Non SUSY AdS W 0 ~10 -10 W 0 <10 -11 Both minima merge

12. Soft SUSY Breaking From KKLT not explicit model but interesting general behaviour (D/F term breaking, AMSB, …) From lifting of large volume models Ms~10 13 GeV Gaugino masses ~ 10 2 GeV, scalars m ~ 10 7 GeV Ms=M GUT viable if warping, Ms=Tev `viable’ if SM anti D-brane (but 5 th force and cmp?) CFNOP,CJO CQS Matter on D3

13. INFLATION Racetrack Inflation Topological eternal inflation ! Slow roll if 1/1000 fine tuning, N~60, δ H ~10 -5 for Ms~10 15 GeV n s ~ 0.95 B-PBCEG-RKLQ

14. D3 Brane φ φ inflaton field Brane- Antibrane inflation BMNRQZ, DSS KKLMMT, HKP, KTW, FT, BCSQ

15. Slow-roll (large field) inflation possible. Need 1/1000 fine tuning of parameters to get 60-efoldings (η-problem) N~60, δ H ~10 -5 for Ms~ 10 15 GeV n s ~1.05 BCSQ

16. V Y tachyon Tachyon complex topological defects D (p-2) branes cosmic strings ! End of inflation: Open string tachyon BMNQRZ ST, JST, CMP S, BMNQRZ

17. Warped tachyonic inflation 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 R, CQS

18. INITIAL CONDITIONS Sen’s open string completeness conjecture t -t Pre big-bang ! ? Inflation and compactification or big-crunch/bang and decompactification ! ? and decompactification ! ?

19. CONCLUSIONS Exciting times RS warping from CS sector, ADD large extra dimensions from Kähler moduli sector. Soft terms calculable for first time rich phenomenology Extensions to other string theories Concrete models of inflation Simple principles, complicated solutions, but SM is also ugly! Many open questions (A fully realistic model?)