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Understanding Large Volume Scenario and Cosmological Implications

Delve into the realization and significance of the Large Volume Scenario in cosmology, exploring topics like realistic models, modular stabilization, and the implications for the Standard Model. Discover insights into string theory, inflation, and moduli fields. Uncover the complexities of cosmological moduli problems, compactifications, and the interplay between different moduli in the universe. This comprehensive overview provides a deep understanding of these intricate cosmological dynamics.

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Understanding Large Volume Scenario 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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