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The LARGE Volume Scenario: Realisation and Cosmological Implications

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. String Phenomenology.

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The LARGE Volume Scenario: Realisation and Cosmological Implications

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  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 M2Planck=M2string V V=104 Mstring=MGUT=1017GeV V=1030 Mstring=1 TeV V=1015 Mstring=1011GeV (Also RS warping !)

  4. MODULI STABILISATION?

  5. Exponentially Large Volumes in IIB

  6. Perturbative vs Non perturbative : • In general: • Then: • Usually V0 dominates but V0=0 (no-scale ) • Dominant term is VJ unless W0<<1(KKLT)

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

  8. as~2π/gs N Exponentially large volumen !!! String scale: Ms2=M2Planck/V W0~1-10 Ms=1 TeV problematic from 5th force

  9. Universe D3 Brane or D7 Brane

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

  11. The Standard Model in the CY

  12. 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

  13. General Conditions for LARGE Volume • h12 > h11 > 1 • 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!

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

  15. Example 1 Blumenhagen et al TauSM

  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 W W Volume, W

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

  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? Ross et al, … Conlon, Kallosh, Linde, FQ

  25. No Overshooting problem!!!

  26. New Candidate Inflatons • L=h11-Nsmall-1 `almost’ flat directions are light • Mass=V-5/3< Volume modulus mass m=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: Volume axion m~exp(-V)<<10-33 eV (equality if Mstring=MGUT)!

  29. Summary of couplings

  30. 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 and decay fast ! (No CMP nor gravitino overproduction) Volume: (mass MeV) CMP Gamma rays, e+-e-

  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 • Nsmall heavy Kahler moduli (cosmological harmless) • Volume modulus (CMP + 511 keV line+ predicted monochromatic line!) (see Boyarski et al) • L=h11-Nsmall-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 (Nsmall) • 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

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