1. The LARGE Volume Scenario: Realisation and Cosmological Implications M. Cicoli, J. Conlon, FQ, 0708.1873 [hep-th] + to appear J. Conlon, R. Kallosh, A. Linde, FQ, to appear F. Quevedo, Cambridge. Liverpool, March 2008. Related talks: E. Plauschinn and E. Palti

2. String Phenomenology Explicit Realistic Models (SU(3)xSU(2)xU(1), 3 families, etc.) Model Independent Issues (axions, no-global symmetries,….,SUSY breaking, moduli stabilisation,…) 4D Effective Actions (Explicit form of K, W, f. For N=1 compactifications)

3. Why LARGE volume? Effective field theory robust Phenomenology M 2 Planck =M 2 string V V=10 4 M string =M GUT =10 17 GeV V=10 30 M string =1 TeV V=10 15 M string =10 11 GeV (Also RS warping !)

4. MODULI STABILISATION?

5. Exponentially Large Volumes in IIB

6. Perturbative vs Non perturbative : In general: Then: Usually V 0 dominates but V 0 =0 (no-scale ) Dominant term is V J unless W 0 <<1 (KKLT)

7. Exponentially Large Volumes Perturbative (alpha’) corrections to K At least two Kähler moduli (h 21 >h 11 >1) Example : BBCQ, CQS (2005)

8. String scale: M s 2 =M 2 Planck /V W 0 ~1-10 Ms=1 TeV problematic from 5 th force Exponentially large volumen !!! a s ~2π/g s N

9. Universe D3 Brane or or D7 Brane

10. Standard Model on D7 Branes Solve hierarchy problem M string = 10 11 GeV! W 0 ~1 (no fine tuning) Kahler potential for chiral matter computed Conlon, Cremades, FQ (2006)

11. The Standard Model in the CY

12. Chiral Matter on D7 Branes Soft SUSY Breaking terms Universality!Universality! No extra CP violation!No extra CP violation! M i = m 3/2 / log (Mp/m 3/2 )M i = m 3/2 / log (Mp/m 3/2 ) String scale 10 11 GeVString scale 10 11 GeV Solves hierarchy problem!Solves hierarchy problem! Conlon et al. Simplest case λ=1/3

13. General Conditions for LARGE Volume h 12 > h 11 > 1 At least one blow-up mode (point-like singularity) Blow-up mode fixed by non-perturbative effects, volume by alpha’ corrections For N small blow-up modes, there are L=h 11 -N small -1 flat directions at tree-level These directions are usually lifted by perturbative effects L moduli lighter than volume!

14. String Loop Corrections Berg-Haack-KorsBerg-Haack-Pajer Leading order correction for V is alpha’ but string loops relevant to fix other moduli

15. Tau SM Example 1 Blumenhagen et al

16. Example 2: K3 Fibrations K3 Fibration with 2 Kahler moduli [1,1,2,2,6] model No LARGE volume

17. K3 Fibration with 3 Kahler moduli (one blow- up) tau3 small, tau 1 and tau 2 LARGE

18.  V  Volume, 

19. COSMOLOGY (Inflation, Cosmological moduli problem, etc.)

20. BRANE - ANTIBRANE INFLATION All branes inflate while two approach Inflaton: Open string mode (talks by R. Gregory, M. Haack and H. Stoica)

21. KAHLER MODULI INFLATION Candidate Inflatons: Closed string modes  Kahler Moduli (size/axion)  Small modulus inflaton

22. Kähler Moduli Inflation Calabi-Yau: 21 > 11 h 21 >h 11 >2 volume τnτn V Conlon-FQBond-Kofman-Prokushkin Small field inflation No fine-tuning!! 0.960<n<0.967

23. Open Questions Loop effects tend to spoil flatness Non tensor perturbations (r=T/S<<<1)? Tension phenomenology vs cosmology Gravitino mass 1 TeV/Gravitino mass >> 1 TeV ?? (string scale 10 11 GeV/ string scale ~ GUT scale)

24. Low Energy SUSY vs Inflation Low scale inflation? Runaway before reheating? Conlon, Kallosh, Linde, FQ Ross et al, …

25. No Overshooting problem!!!

26. New Candidate Inflatons L=h 11 -N small -1 `almost’ flat directions are light Mass=V -5/3 < Volume modulus mass m=V -3/2 ~H Recall η ~ mass 2 /H Cicoli et al.

27. After Inflation

28. Physics of Moduli Fields Dilaton and Complex Structure Small (heavy) Kahler moduli Large (light) Kahler modulus Moduli masses: Volume axion m~exp(-V)<<10 -33 eV (equality if M string =M GUT )!

29. Summary of couplings

30. Other Cosmological Implications Cosmological moduli problem Observational implications of light volume modulus? U,S: trapped at their minimum T: except for volume, heavy and decay fast ! (No CMP nor gravitino overproduction) Volume: (mass MeV) CMP Gamma rays, e + -e - J.Conlon, FQ DCQR, BKN

31. The 511 keV Line

32. INTEGRAL/ SPI 511 keV line Light Modulus χ: Dark matter? Mass 1MeV, coupling to electrons dominant 511 keV from volume modulus decay? (prediction!) BUT `almost’ ruled out 2 months ago!!!

33. Intensity INTEGRAL

34. General Picture N small heavy Kahler moduli (cosmological harmless) Volume modulus (CMP + 511 keV line+ predicted monochromatic line!) (see Boyarski et al) L=h 11 -N small -1 lighter moduli (candidate inflatons, CMP, new monochromatic lines!! (observable?)) CMP (late low energy inflation?)

35. Conclusions Non-perturbative effects fix only a fraction of Kahler moduli (N small ) Alpha’ effects fix volume to exponentially large values (Both LARGE volume and large warping in the same class of models!?) Loop corrections needed to fix the rest of Kahler moduli Interesting phenomenology/cosmology Astrophysics (forest of monochromatic lines?) Fully realistic model?

36. Solution of CMP? Thermal Inflation Lyth+Stewart (1995) Number of e-folds N~10 dilutes moduli