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Moduli Stabilisation and Cosmology: Perturbative vs. Non-Perturbative Effects for String Theory

Explore how perturbative and non-perturbative effects affect moduli stabilisation and cosmology in string theory, covering topics such as supersymmetry breaking, scalar potentials, string loop corrections, and large volume scenarios with implications for inflation and dark matter. A comprehensive overview of the interplay between string theory and cosmological models, addressing open questions and potential solutions.

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Moduli Stabilisation and Cosmology: Perturbative vs. Non-Perturbative Effects for String Theory

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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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