1. Cosmology in LARGE volume string models Tetsutaro Higaki arXiv: 1208.3563 published in JHEP 1211 (2012) 125 with Fuminobu Takahashi at Tohoku U. See also arXiv: 1208.3562 by Cicoli, Conlon and Quevedo 01/29/2013@Osaka U.

2. Production of a hot dark matter via LARGE extra dimensions.

3. 1. Motivation: Exploring the origin of the Universe. 1. Introduction

4. The present universe consists of Dark matter and dark energy clearly require new physics beyond the Standard Model (SM). What is the Universe made of?

9. Past and now of the Universe In the early Universe Baryons Dark matter (Cold DM) Photons Neutrinos dominated.

10. Past and now of the Universe In the early Universe Baryons Dark matter (Cold DM) Photons Neutrinos + Dark radiation dominated. Sterile 4 th neutrino-like (A part of hot dark matter)

11. My motivation Dark radiation N eff ～ 4 || A probe of high energy physics!?

12. The Standard ModelModuli & Hidden sectors E.g. Gravity Anomaly cancellation condition Overview of string-theory-models Hidden sectors appear naturally through stringy compactifications!

13. Supergravity models on a LARGE Swiss-cheese Calabi-Yau (CY) SM

14. Main characters in 4D SUGRA 1.Size of CY 3 2.Higgs 3. Axion (Ex-dim.) (DR) 4. Wino (CDM)

15. Contents 1.Introduction: Motivations and short summary 2.Observations and dark Radiation 3.LARGE volume scenario (LVS) 4.Dark radiation and dark matter from the modulus decay 5.Conclusion and open questions

16. 2. Observations of dark radiation (a hot DM)

17. Dark radiation (DR) 4 th neutrino-like component in cosmic ν background Ultralight mass: M DR ≦ m ν ≦ 0.1 eV Almost no interaction: Gravity or… How can we detect the presence indirectly?

18. In radiation-dominated era with T ≦ 1MeV DR DR and expansion of the universe

19. The expansion rate gets increased by ΔN eff. H: Expansion rate (Hubble parameter) The Friedman equation in rad. era DR and expansion of the universe

20. 4 He abundace is sensitive to the expansion rate H at BBN era ～ 1 sec. Cosmic Microwave Background (CMB) is sensitive to H at ～ 380,000 year. Mild DR evidence

22. Cyburt, Fields, Olive (2008)

23. HII region (H +, He*,O*,…)

24. CMB ΔT/T 0 map on the sky sphere, where T 0 = 2.73K. WMAP 9-year

25. CMB Fourier form of ΔT/T 0 map on the sky sphere, where T 0 = 2.73K. WMAP 9-year, 1212.5226

26. South Pole Telescope (SPT) Wilkinson Microwave Anisotropy Probe (WMAP) Atacama Cosmology Telescope (ACT) in Chili

28. Recent other CMB data WMAP 9-year, 1212.5226 : Atacama Cosmology Telescope (ACT), 1301.0824 :

29. Recent other CMB data WMAP 9-year, 1212.5226 : Atacama Cosmology Telescope (ACT), 1301.0824 : – Fewer # of data – Different frequency in CMB Note: Tension between BAO and H 0. Wrong!!; will be modified.

30. Adoption of SPT result So, both 4 He abundance and CMB mildly prefer the presence of extra radiation:

31. in 4D N=1 supergravity (SUGRA) framework. For confirmation of dark radiation WMAP 9-year, 1212.5226 Needs data from the Planck.

32. 3. LARGE volume scenario (LVS): IIB orientifold supergravities in flux vacua

33. Motivation for string theory Unified theory including quantum gravity! Closed string Gravity = Gravity Open string Gauge = Gauge D-brane Open string between branes Matter = Matter nucleons

34. Extra dimensions and SUSY The quantum gravity theory requires extra 6 dimensions and supersymmetry (SUSY). M 4 × 4+6=10

35. The Standard ModelModuli & Hidden sectors E.g. Gravity Anomaly cancellation condition Phenomenological motivation Hidden sectors appear naturally through stringy compactifications!

36. Moduli in a Calabi-Yau space SUSY-preserved compactification

37. 4-cycle size: T (Kähler moduli) 3-cycle size: U (Complex structure moduli) + String Dilaton: S Moduli in a Calabi-Yau space SUSY-preserved compactification

38. Why moduli and axions? 1.Ubiquitous in string vacua. 2.VEVs = physical constants: Size of extra dimension; Gauge/Yukawa couplings, SUSY-breaking parameters.

39. Moduli ～ gauge couplings (Ex) (4+n) dim. gauge theory on a brane (M 4 ×Σ n ):

40. Moduli ～ gauge couplings (Ex) (4+n) dim. gauge theory on a brane (M 4 ×Σ n ): Modulifield φ Moduli field φ : Volume of a cycle

41. Moduli ～ gauge couplings (Ex) (4+n) dim. gauge theory on a brane (M 4 ×Σ n ): Modulifield φ Moduli field φ : Volume of a cycle An extra 6 dimension space can have many Σ n. ↓ Many moduli

42. Axions ～ θ-term (Ex) (4+n) dim. gauge theory on a brane (M 4 ×Σ n ):

43. Axions ～ θ-term (Ex) (4+n) dim. gauge theory on a brane (M 4 ×Σ n ): Axion field a Axion field a: Integrand of tensor field C n (NSNS, RR)

44. Axions ～ θ-term (Ex) (4+n) dim. gauge theory on a brane (M 4 ×Σ n ): An extra 6 dimension space can have many Σ n. ↓ Many axions Axion field a Axion field a: Integrand of tensor field C n (NSNS, RR)

45. What are their masses? What are their VEVs? (= couplings etc.) Moduli/axion stabilization

46. Flux compactifications Flux compactifications with O-planes and D-branes

47. Moduli/axion stabilization Finding a vacuum of moduli in a string model

48. Example of potential for moduli

49. Ultralight axion(s) In a LARGE volume limit of compact space, axion will get ultralight thanks to a residual gauge symmetries on C n in 10D: The axions originate from gravity C n (NSNS or RR-field).

50. Model: LARGE volume scenario (LVS) V. Balasubramanian, P. Berglund, J. P. Conlon and F. Quevedo.(2005); R. Blumenhagen, J. P. Conlon, S. Krippendorf, S. Moster and F. Quevedo.(2009)

51. Cartoon of LVS models: Swiss cheese Calabi-Yaus 418 Note: 418 such explicit CY models; a single hole model J. Gray, Y.H. He, V. Jejjala, B. Jurke, B. Nelsond and J. Simon (2012) Intersection # among 2cycles is important.

52. 418 Note: 418 such explicit CY models; a single hole model J. Gray, Y.H. He, V. Jejjala, B. Jurke, B. Nelsond and J. Simon (2012) Instantons 3-form Flux Moduli stabilization for volume, holes, shapes. Cartoon of LVS models: Swiss cheese Calabi-Yaus

53. 418 Note: 418 such explicit CY models; a single hole model J. Gray, Y.H. He, V. Jejjala, B. Jurke, B. Nelsond and J. Simon (2012) Local model Local model: MSSM + U(1) A on D3-branes. It is on a singularity, which is stabilized by FI=0. QLQL QRQR L eReR U(2) U(3) U(1) Cartoon of LVS models: Swiss cheese Calabi-Yaus

54. Matter content of the MSSM (Minimal Supersymmetric Standard Model) R-parity(Superpartner)= -1 R-parity(SM-particles)= +1

55. Model details

56. Notation for 4D N=1 SUGRA Lagrangian: K : Kähler potential, W: Superpotential f : gauge coupling function,

57. Volume moduli stabilization in LVS T b : Overall volume + DR T s : Hole volume + heavy axion

58. Scalar potential Other moduli can be irrelevant in this analysis. a s =2π τ s = Re(T s ) V pot

59. Exponentially LARGE volume CY LARGE moduli VEV: ξ =O(1) ∝ χ(CY) : A choice of Swiss cheese CY. g s =O(0.1) : A choice of quantized flux. Note: SUSY-breaking AdS; needs ΔV pot ～ Vol(CY) -3 for dS/Mink.

60. Masses: Gravitino and the lightest modulus SUSY-breaking parameters on D3-branes (local): CY volume controls everything

61. Mass scales Overall volume: ～ 10 6 GeV Overall volume: ～ 10 6 GeV Holes (volume): ～ 10 12 GeV Shape: ～ 10 11 GeV ～ gravitino mass Singularity: ～ 10 15 GeV ～ string scale Volume (CY) = O(10 7 ) for Volume (CY) = O(10 7 ) in string unit; 1/R= O(10 13 ) GeV

62. Mass scales Overall volume: ～ 10 6 GeV Overall volume: ～ 10 6 GeV Holes (volume): ～ 10 12 GeV Shape: ～ 10 11 GeV ～ gravitino mass Singularity: ～ 10 15 GeV ～ string scale Volume (CY) = O(10 7 ) for Volume (CY) = O(10 7 ) in string unit; 1/R= O(10 13 ) GeV Instantons (ED3-branes) 3-form Flux

64. A dark radiation candidate in LVS TH, Takahashi; Cicoli, Conlon, Quevedo (2012) a b := Im(T b ): Axion as dark radiation stays ultralight even if we have where Re(T b )= Vol(CY) 2/3 = 10 5 >>1. is only gravitationally interacting.

65. 5. Dark radiation and dark matter from the modulus decay TH, Takahashi See also Cicoli, Conlon, Quevedo

66. Why modulus decay? Answer: It reheats the universe, producing DM and DR. : Canonically-normalized fluctuation of T b

67. Moduli problem in LVS Before inflation, modulus will be in the vacuum

68. Inflation produces additional potential for φ Moduli problem in LVS

69. During inflation, modulus is sitting false vacuum Moduli problem in LVS

70. During inflation, modulus is sitting false vacuum Moduli problem in LVS

71. For H inf > m φ1 decompactification occurs. Moduli problem in LVS

72. For H inf > m φ1 decompactification occurs. is required. Moduli problem in LVS

73. At the end of inflation, inflaton contribution will vanish. Moduli problem for H inf ≦ m φ1 TH, Kamada, Takahashi

74. At the end of inflation, modulus starts to oscillate for m Inflaton > m φ1. Amplitude: Moduli problem for H inf ≦ m φ1 TH, Kamada, Takahashi

75. At the end of inflation, modulus starts to oscillate for m Inflaton > m φ1. Energy (matter-like): Moduli problem for H inf ≦ m φ1 TH, Kamada, Takahashi

76. from inflaton decay Moduli decay: New radiation at H = Γ φ1 At the end of inflation, Modulus starts to oscillate H inf ≦ m φ1 ＜ m inflaton

77. Modulus decay in LVS and No-scale z: Coefficient for higgsino mass (μ-term) V= Re(T b ) 3/2 : Swiss-cheese CY volume W matter : Yukawa-terms for matter Q i bb

79. Modulus decay into Higgs and axions Decay width of modulus φ 1 Reheating temperature and branching to DR

80. n H : The total number of Higgs multiplets z 2 ⇔ n H Decay width of modulus φ 1 with z=1 Partial decay width to DR with z=1 If there are additional Higgses,…

81. Dark radiation vs z (n H =1) m φ ～ V -3/2 ΔN eff obs ～ 1

82. Gauge-Higgs Unification in SUSY? We have z ～ 1 (tanβ ～ 1), if K ～ |H u + H d † | 2 with a shift symmetry H u → H u + ic, H d → H d + ic. Hebecker et al. Non-chiral Higgs pair

83. Dark matter: Wino (With assumed R-parity)

84. DM: Motivation for SUSY R-parity(Superpartner)= -1 R-parity(SM-particles)= +1 DM = Wino is assumed

85. Modulus decay into Wino DM φ1φ1 HuHu HdHd Br = O(1)

86. Modulus decay into Wino DM HuHu HdHd Br = O(0.01) ～ 1/N channel for m 0 = 1/V 2 = O(10) TeV, μ ～ M 1/2 = 1/log(V)V 2 = O(1) TeV.

87. Wino DM pair annihilation These process hardly depends on the branching fraction.

88. Wino abundance Ω wino h 2 vs z (Ω CDM h 2 ) obs ～ 0.1 For z ～ 1.5, ΔN eff ～ 1 m Wino ～ 500GeV

89. Moroi, Nakayama (2011) Constraint on Wino-like DM mass m Wino ≧ 500 GeV!

90. DR and DM from modulus decay Higgs from φ 1 DR (no-scale), DM (the decay) For z ～ 1.5 or 2-3 ×(H u, H d ) with each z = 1, DR can be explained. For m Wino ～ 500 GeV, DR and DM are explained. If higgsino is DM, they are too many produced.

91. 6.Conclusion and open questions

92. Production of a hot dark matter via LARGE extra dimensions.

93. LARGE Swiss-cheese CY in the cosmos LARGE Volume modulus : φ

94. The φ decay: φ→ Higgs + axions + Wino in 4D N=1 supergravity (SUGRA) framework. Summary of cosmology

95. The φ decay: φ→ Higgs + axions + Wino reheats the universe at T dec ～ 1GeV. in 4D N=1 supergravity (SUGRA) framework. Summary of cosmology

96. The φ decay: φ→ Higgs + axions + Wino reheats the universe at T dec ～ 1GeV. also produces DR of string-theoretic axions. LARGE volume CY: Ultralight axion and No-scale LARGE volume CY: Ultralight axion and No-scale in 4D N=1 supergravity (SUGRA) framework. Summary of cosmology

97. The φ decay: φ→ Higgs + axions + Wino reheats the universe at T dec ～ 1GeV. also produces DR of string-theoretic axions. LARGE volume CY: Ultralight axion and No-scale LARGE volume CY: Ultralight axion and No-scale also produces DM of Winos (with assumed R-parity). in 4D N=1 supergravity (SUGRA) framework. Summary of cosmology

98. in 4D N=1 supergravity (SUGRA) framework. For confirmation of dark radiation WMAP 9-year, 1212.5226 Needs data from the Planck.

99. Many open questions Concrete stringy realization? Vacuum selection rule? Reconsideration of “naturalness”?: M new phys >> TeV ?

100. Swiss-cheese can be useful not only for “food life” but also for “our lives” in the cosmos.

101. Thank you!

102. Backup

103. 100points of HII regions (Ionized hydrogen: T ～ 10 4 K) Y p vs Oxygen Spectra analysis Steigman (2012) (Time?: O needs time for production)

104. Tension in H 0 observations WMAP 9-year, 1212.5226