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Perturbative vs Non-Perturbative Effects for Moduli Stabilisation and Cosmology

Perturbative vs Non-Perturbative Effects for Moduli Stabilisation and Cosmology. J. Conlon, FQ 0705.3460 [hep-ph] M. Cicoli, J. Conlon, FQ, 0708.1873 [hep-th] + to appear J. Conlon, R. Kallosh, A. Linde, FQ, to appear. F. Quevedo, Cambridge. MPI 2007.

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Perturbative vs Non-Perturbative Effects for Moduli Stabilisation and Cosmology

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  1. Perturbative vs Non-Perturbative Effects for Moduli Stabilisation and Cosmology J. Conlon, FQ 0705.3460 [hep-ph] M. Cicoli, J. Conlon, FQ, 0708.1873 [hep-th] + to appear J. Conlon, R. Kallosh, A. Linde, FQ, to appear F. Quevedo, Cambridge. MPI 2007.

  2. Moduli Stabilisation and Supersymmetry Breaking

  3. 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 MinimumDaW = 0Fixes Ua and S T moduli unfixed:No-Scale models KKLT Scenario …GKP, KKLT, … Size of cycle a = Ua GKP

  4. To fix Kähler moduli: Non-perturbative D7 effects Non-perturbative Fluxes Volume SUSY AdS minimum (W0 << 1)

  5. ALL MODULI STABILISED !?

  6. Exponentially Large Volumes

  7. Argument: • In general: • Then: • Usually V0 dominates but V0=0 (no-scale ) • Dominant term is VJ unless W0<<1(KKLT)

  8. Exponentially Large Volumes BBCQ, CQS (2005) • Perturbative (alpha’) corrections to K • At least two Kähler moduli (h21>h11>1) Example :

  9. as~2π/gs N Exponentially large volumen !!! String scale: Ms2=M2Planck/V W0~1-10 Robustness: CQS, C (2005), BHP (2007)

  10. General Conditions for LARGE Volume • h12 > h11 • At least one blow-up mode (point-like singularity) • Blow-up mode fixed by non-perturbative effects, volume by alpha’ corrections • For Nsmall blow-up modes, there are L=h11-Nsmall-1 flat directions at tree-level • These directions are usually lifted by perturbative effects L moduli lighter than volume!

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

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

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

  14. PHENOMENOLOGY (LARGE Volume)

  15. The Standard Model in the CY

  16. Standard Model on D7 Branes • Solve hierarchy problem Mstring = 1011GeV! • W0~1 (no fine tuning) • Kahler potential for chiralmatter computed Conlon, Cremades, FQ (2006)

  17. Chiral Matter on D7 Branes Soft SUSY Breaking terms Conlon et al. • Universality! • No extra CP violation! • Mi = m3/2 / log (Mp/m3/2) • String scale 1011 GeV • Solves hierarchy problem! Simplest case λ=1/3

  18. Stringy source of universality(approximate) See: Conlon 0710.0873 [hep-th] Approximate no-scale + locality Also: Anomaly mediation suppressed !!! CP Violation Physical phases vanish !

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

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

  21. Kähler Moduli Inflation Conlon-FQ Bond-Kofman-Prokushkin Calabi-Yau: h21>h11>2 Small field inflation No fine-tuning!! 0.960<n<0.967 V τn volume

  22. 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)

  23. Possible ways out • Low scale inflation? • Runaway before reheating? Ross et al, … Conlon, Kallosh, Linde, FQ

  24. Runaway + Oscillations after inflation

  25. No Overshooting problem!!!

  26. New Candidate Inflatons • L=h11-Nsmall-1 `almost’ flat directions are light • Mass < Volume modulus mass=V-3/2~H • Recall η ~ mass2/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:

  29. Physical Fields Decay Rates

  30. Summary

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

  32. The 511 keV Line

  33. INTEGRAL/ SPI 511 keV line Light Modulus χ: Dark matter? Mass 1MeV, coupling to electrons dominant 511 keV from volume modulus decay? (prediction!)

  34. Intensity INTEGRAL

  35. General Picture • Nsmall heavy Kahler moduli (cosmological harmless) • Volume modulus (CMP + 511 keV line+ predicted monochromatic line) • L lighter moduli (candidate inflatons, CMP, new monochromatic lines!! (observable?)) • CMP (late low energy inflation?)

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

  37. Conclusions • Non-perturbative effects fix only a fraction of Kahler moduli (Nsmall) • Alpha’ effects fix volume to exponentially large values • Loop corrections needed to fix the rest of Kahler moduli • Interesting cosmology (gravitino mass problem + overshooting problem can be handled, still some tuning) • Astrophysics (forest of monochromatic lines)

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