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Cosmology and String Theory

Cosmology and String Theory. F. Quevedo Cambridge CORFU 2005. OUTLINE. String Cosmology before 2003 The KKLT Scenario and the String Landscape Inflation and Moduli Stabilization. FQ hepth/0210292. STRING COSMOLOGY.

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Cosmology and String Theory

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  1. Cosmology and String Theory F. Quevedo Cambridge CORFU 2005

  2. OUTLINE • String Cosmology before 2003 • The KKLT Scenario and the String Landscape • Inflation and Moduli Stabilization FQ hepth/0210292

  3. STRING COSMOLOGY • String theory is fundamental then it should have important implications in early universe • Quantum gravity Big bang or before • Experimental tests of the theory?

  4. OBSERVATIONAL CHALLENGES

  5. CMB Anisotropies

  6. EXPERIMENTALEVIDENCE FOR Λ>0 Ω = ΩΛ + ΩM + ΩK = 1 Ω = ρ/ρc relative energy density K = -1,0,1 open, flat, closed universe ΩΛ~ 0.7, ΩM~ 0.3, Ωk~ 0

  7. PROBLEM Do not understand the theory in time dependent backgrounds !!!

  8. Effective Field Theories

  9. General Aspects • Branderberger-Vafa Scenario ((S1)9 x time) T-duality Minimal distance ! Winding modes D=4 (since 2+2=4)!

  10. Gasperini, Veneziano,… • Pre Big-Bang Cosmology t=0 singularity + strong coupling

  11. String Theory and 4D Inflation

  12. MOTIVATION • Inflation: very successful but only scenarios in search of a theory • String theory: fundamental theory but lacks experimental tests. • Is it possible to `derive’ inflation from string theory?

  13. Need to compute scalar potential from String theory satisfying slow-roll conditions: Number of e-folds N>60 Density perturbations

  14. HISTORY • t<1986 Calabi-Yau String Compactifications: Many free moduli (size and shape of extra dimensions) from gmn, Bmn, φ, AmI • 1986<t<1991 Geometric moduli: candidate for inflaton fields. But no potentials (V=0). Or V too steep: Candelas et al. Dilaton S, Kähler T Complex structure U Wilson lines W Binetruy-Gaillard, Banks et al Brustein-Steinhardt

  15. New Problems: Overshooting (natural to end up in runaway) Cosmological Moduli Problem (moduli overclose the universe or ruin nucleosynthesis) Brustein-Steinhardt Coughlan et al. Banks et al. De Carlos et al.

  16. t=1995-1998The Brane World ADD, Horava-Witten,…

  17. t=1998 More moduli! : D-brane inflation. But V=0 or non-calculable. t=2001 Brane/Antibrane inflation: Dvali-Tye Burgess et al., Dvali et al Generically no slow roll, but…

  18. End of inflation: Open string tachyon Burgess et al. V tachyon Y Tachyon complex topological defects D (p-2) branes cosmic strings ! Sen, Burgess et al. Tye et al. Copeland et al.

  19. Intersecting Brane Inflation Garcia-Bellido et al. Y: Inflaton End of inflation: tachyon Also: D3-D7 inflation Kallosh et al.

  20. Ekpyrotic/Cyclic Scenario Horava Witten 11D a(0)=0 weak coupling (bounce?) But: singularity? Potential by hand,…

  21. Outstanding Problem • Moduli Stabilization A Solution: turn-on fluxes t> 2003 KKLT Scenario …GKP, KKLT, …

  22. Moduli Stabilization

  23. The Problem • String/M-Theory unique but has many solutions or vacua. • Some solutions resemble the Standard Model and MSSM. • Degeneracy : Discrete + Continuous (SUSY) . • Outstanding Problems: SUSY breaking + Vacuum degeneracy.

  24. History • t<1986 Calabi-Yau String Compactifications: Many free moduli (size and shape of extra dimensions) • 1986<t<1991 Gaugino condensation and T-duality • 1991<t<2002 More moduli! (D-brane positions) • t>2002 GKP/ KKLT : Fluxes fix moduli Dilaton S, Kähler T Complex structure U CHSW Fix S and one T DIN, DRSW, K, FILQ, FMTV …GKP, KKLT, …

  25. 4D Compactifications + Fluxes

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

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

  28. Multi-throat compactification

  29. Lifting to de Sitter (add anti D3 branes, D-terms, etc.) KKLT, BKQ, SS, VZ SUSY breaking term V axion volume

  30. The Landscape • Huge number of discrete vacua >10500 • Statistics • Randall-Sundrum warping from strings! • Non SUSY de Sitter • Dark energy? • `SM’ on D3/D7branes • Soft SUSY breaking? • Inflation? AD, DD, DDF, GKTT,CQ,BGHLW GKP BP CG-MQU

  31. Populating the Landscape Classical Solutions Quantum decay (tunnel efect)

  32. Multiverse and Eternal Inflation

  33. Realistic Models CG-MQU, CSU

  34. Exponentially Large Volumes BBCQ, CQS • At least two Kähler moduli (h21>h11>1) • Perturbative corrections to K Example : Exponentially large !

  35. Non SUSY AdS W0~1-10 String scale: Ms2=Mp2/V

  36. KKLT AdS Non SUSY AdS Both minima merge W0~10-10 W0<10-11

  37. Soft SUSY Breaking • From KKLT not explicit model but interesting general behaviour (D/F term breaking, AMSB, …) • From lifting of large volume models CFNOP,CJO CQS Matter on D3 Ms~1013 GeV Gaugino masses ~ 102 GeV, scalars m ~107 GeV Ms=MGUT viable if warping, Ms=Tev `viable’ if SM anti D-brane (but 5th force and cmp?)

  38. Inflation and Moduli Stabilization

  39. Brane-Antibrane Inflation KKLMMT, HKP, KTW, FT, BCSQ, … φ inflaton field D3 Brane φ

  40. Slow-roll (large field) inflation possible. Need 1/1000 fine tuning of parameters to get 60-efoldings (η-problem) N~60, δH~10-5 for Ms~ 1015 GeV ns~1.05 Burgess, Cline, Stoica, FQ Needs at least two throats ! Kallosh et al. Also: D3-D7 on K3xT2 DBI in the sky Silverstein-Tong, Chen

  41. Warped Tachyonic Inflation Sen, Raeymakers, Cremades-Sinha-FQ A,B depend on warping (fluxes) and E&M fields on non-BPS brane. If A,B~1 no slow-roll AB large slow-roll No fine-tuning! But need large fluxes

  42. INITIAL CONDITIONS Sen’s open string completeness conjecture t -t Pre big-bang ! ? Inflation and compactification or big-crunch/bang and decompactification ! ?

  43. Racetrack Inflation Blanco-Pillado et al. Topological eternal inflation ! Slow roll if 1/1000 fine tuning, N~60, δH~10-5 for Ms~1015 GeV ns~ 0.95 Also for W0=0 if add matter Lalak, Ross, Sarkar

  44. Improved Racetrack Blanco-Pillado et al. Douglas et al. Explicitly derived model Similar physics

  45. Kähler Moduli Inflation Conlon-FQ Any Calabi-Yau: h21>h11>2 V Large field inflation No fine-tuning!! 0.960<n<0.967 τn volume

  46. CONCLUSIONS • Exciting times • Type IIB: Several inflationary scenarios, Inflaton: Kahler modulus, brane sparation, tachyon, Wilson lines , Complex structure moduli (?). • Reheating • Extensions to other string theories (Becker et al) • Initial conditions • Overshooting problem,…. OPEN QUESTIONS

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