A Minimal Supersymmetric Cosmological Model

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1 A Minimal Supersymmetric Cosmological Model Ewan Stewart KAIST COSMO/CosPA 2010 University of Tokyo 29 September 2010 EDS, M Kawasaki, T Yanagida D Jeong, K Kadota, W-I Park, EDS G N Felder, H Kim, W-I Park, EDS R Easther, J T Giblin, E A Lim, W-I Park, EDS S Kim, W-I Park, EDS hep-ph/ hep-ph/ hep-ph/ arxiv: arxiv:

2 Standard model of cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl GeV ν R decay matter/antimatter? s 10 3 GeV 100 kev electroweak transition neutralino freeze out QCD transition nucleosynthesis matter/antimatter? neutralino dark matter? axion dark matter? light elements s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration yr time

3 Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains n s to 10 15

4 Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s to H 2 (Ψ Ψ 1 ) 2

5 Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s to H 2 (Ψ Ψ 1 ) 2 m 2 susy (Ψ Ψ 0 ) 2 M Pl

6 Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s to n s 107 m 2 susy (Ψ Ψ 0 ) 2 M Pl

7 Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s to n s 107 m 2 susy (Ψ Ψ 0 ) 2 M Pl Moduli generated: H m susy

8 Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s to n s 107 m 2 susy (Ψ Ψ 0 ) 2 M Pl Moduli generated: H m susy slow-roll inflation: H m inflaton m susy

9 Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s to n s 107 m 2 susy (Ψ Ψ 0 ) 2 M Pl Moduli generated: H m susy after slow-roll inflation: H m inflaton m susy

10 Standard model of cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl GeV ν R decay matter/antimatter? s 10 3 GeV 100 kev electroweak transition neutralino freeze out QCD transition nucleosynthesis matter/antimatter? neutralino dark matter? axion dark matter? light elements s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration yr time

11 Standard model of cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl GeV ν R decay moduli, gravitinos,... matter/antimatter? disaster s 10 3 GeV 100 kev electroweak transition neutralino freeze out QCD transition nucleosynthesis matter/antimatter? neutralino dark matter? axion dark matter? light elements s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration yr time

12 Minimal Supersymmetric Standard Model W = λ u QH u ū + λ d QH d d + λe LH d ē + µh u H d

13 Minimal Supersymmetric Standard Model W = λ u QH u ū + λ d QH d d + λe LH d ē + µh u H d But µ? neutrino masses? strong CP?

14 Minimal Supersymmetric Cosmological Model W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ

15 Minimal Supersymmetric Cosmological Model MSSM W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ

16 Minimal Supersymmetric Cosmological Model MSSM neutrino masses W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ

17 Minimal Supersymmetric Cosmological Model MSSM neutrino masses MSSM µ-term W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ µ = λ µ φ 2 0

18 Minimal Supersymmetric Cosmological Model MSSM neutrino masses MSSM µ-term drives m 2 φ < 0 W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ µ = λ µ φ 2 0 V 0 V φ 0 φ

19 Minimal Supersymmetric Cosmological Model MSSM neutrino masses MSSM µ-term drives m 2 φ < 0 W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ µ = λ µ φ 2 0 axion V 0 V φ 0 φ

20 Thermal inflation V V 0 RADIATION DOMINATION φ 0 φ

21 Thermal inflation V V 0 THERMAL INFLATION φ 0 φ

22 Thermal inflation V V 0 THERMAL INFLATION φ 0 φ

23 Thermal inflation V V 0 first order phase transition φ 0 φ

24 Thermal inflation V V 0 potential energy converted to particles φ 0 φ

25 Thermal inflation V V 0 MATTER DOMINATION φ 0 φ

26 Key properties of thermal inflation For φ to GeV

27 Key properties of thermal inflation For Large dilution φ to GeV = pre-existing moduli sufficiently diluted

28 Key properties of thermal inflation For Large dilution φ to GeV = pre-existing moduli sufficiently diluted Short duration N 10 = primordial perturbations from slow-roll inflation preserved on large scales

29 Key properties of thermal inflation For Large dilution φ to GeV = pre-existing moduli sufficiently diluted Short duration N 10 = primordial perturbations from slow-roll inflation preserved on large scales Low energy scale V 1/ to 10 7 GeV = moduli regenerated with sufficiently small abundance

30 Gravitational waves Ω GW DECIGO INFLATION PREHEATING PRIMORDIAL INFLATION f Hz

31 Gravitational waves 10 5 Ω GW DECIGO PRIMORDIAL INFLATION THERMAL INFLATION INFLATION PREHEATING f Hz

32 Baryogenesis Key assumption mlh 2 u = 1 ( m 2 2 L + mh 2 ) u < 0

33 Baryogenesis Key assumption m 2 LH u = 1 2 ( m 2 L + m 2 H u ) < 0 Implies a dangerous non-mssm vacuum with LH u (10 9 GeV) 2 and λ d QL d + λ e LLē = µlh u eliminating the µ-term contribution to LH u s mass squared. V our vacuum deeper vacuum 0 LH u, QL d, LLē

34 Reduction W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ

35 Reduction W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ ( L = l e/ 2 ) ( 0, H u = ū = ( ) (, Q = h u ), H d = d/ ) ( hd 0 φ = φ, χ = 0, χ = 0 ), ē = ( e/ 2 ), d = ( d/ )

36 Potential V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 m 2 φ φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2

37 Potential drives thermal inflation V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 m 2 φ φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2

38 Potential drives thermal inflation lh u rolls away V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 m 2 φ φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2

39 Potential drives thermal inflation lh u rolls away V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 m 2 φ φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 lh u stabilized with fixed phase + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2

40 Potential drives thermal inflation lh u rolls away φ rolls away V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 m 2 φ φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 lh u stabilized with fixed phase + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2

41 Potential drives thermal inflation lh u rolls away φ rolls away V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 m 2 φ φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 lh u stabilized with fixed phase + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2 h d forced out

42 Potential drives thermal inflation lh u rolls away φ rolls away V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 m 2 φ φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 lh u stabilized with fixed phase + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2 d and e held at origin h d forced out

43 Potential drives thermal inflation lh u rolls away φ rolls away V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 m 2 φ φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 lh u stabilized with fixed phase + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2 d and e held at origin lh u returns with rotation h d forced out

44 Potential drives thermal inflation lh u rolls away φ rolls away φ stabilized m 2 φ (φ 0) = α φ m 2 φ (0) V 0 + m 2 L l 2 m 2 H u h u 2 + m 2 H d h d 2 + m 2 d d 2 + m 2 e e 2 + m 2 φ(φ) φ 2 [ A νλ ν l 2 hu A dλ d h d d 2 1 ] 2 A eλ e h d e 2 A µ λ µ φ 2 h u h d + c.c. + λ ν lhu λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u λ dd λ ee 2 lh u stabilized with fixed phase + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d g 2 ( h u 2 h d 2 l d e 2 ) 2 d and e held at origin lh u returns with rotation h d forced out

45 Baryogenesis MODULI DOMINATION φ = 0 h u h d = 0 lh u = 0 THERMAL INFLATION FLATON DOMINATION RADIATION DOMINATION φ > 0 φ φ 0 φ preheats φ decays h d > 0 d = e = 0 lh u > 0 brought back into origin with rotation n L < 0 nucleosynthesis preheating and thermal friction N L conserved l, h u, h d decay T > T EW n L n B dilution n B /s 10 10

46 Numerical simulation n L /n AD mt

47 Baryon asymmetry n B s n L n AD T d n AD n φ m φ (φ 0 )

48 Baryon asymmetry Using n B s n L n AD T d n AD n φ m φ (φ 0 ) n φ m φ (φ 0 ) φ 2 0, m 2 φ(φ 0 ) α φ m 2 φ(0), n AD m LHu l 2 0 l GeV (10 2 ev m ν ) (mlhu TeV ) gives ( ) ( ) 2 GeV µ T d 1 GeV TeV φ 0 n B s ( nl /n AD 10 2 ) ( ) 3 ( GeV 10 2 ev φ 0 m ν ) ( µ TeV ) 2 ( 10 1 α φ ) ( mlhu m φ (0) ) 2

49 Baryon asymmetry Using n B s n L n AD T d n AD n φ m φ (φ 0 ) n φ m φ (φ 0 ) φ 2 0, m 2 φ(φ 0 ) α φ m 2 φ(0), n AD m LHu l 2 0 l GeV (10 2 ev m ν ) (mlhu TeV ) gives ( ) ( ) 2 GeV µ T d 1 GeV TeV φ 0 n B s ( nl /n AD 10 2 ) ( ) 3 ( GeV 10 2 ev φ 0 m ν ) ( µ TeV ) 2 ( 10 1 α φ ) ( mlhu m φ (0) ) 2 which suggests φ GeV

50 Dark matter candidates Peccei-Quinn symmetry W = λ u QH u ū +λ d QH d d +λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ

51 Dark matter candidates Peccei-Quinn symmetry DFSZ axion W = λ u QH u ū +λ d QH d d +λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ

52 Dark matter candidates Peccei-Quinn symmetry DFSZ axion KSVZ axion W = λ u QH u ū +λ d QH d d +λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ

53 Dark matter candidates Peccei-Quinn symmetry DFSZ axion KSVZ axion W = λ u QH u ū +λ d QH d d +λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ Axion m a Λ2 QCD 2 φ0 where f a = f a N ( ) GeV ev f a

54 Dark matter candidates Peccei-Quinn symmetry DFSZ axion KSVZ axion W = λ u QH u ū +λ d QH d d +λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ Axion m a Λ2 QCD 2 φ0 where f a = f a N ( ) GeV ev f a Axino mã = 1 16π 2 λ 2 χa χ χ 1 to 10 GeV

55 Dark matter genesis thermal inflation

56 Dark matter genesis thermal inflation first order phase transition flaton = saxino matter domination

57 Dark matter genesis thermal inflation first order phase transition flaton = saxino matter domination decay radiation domination

58 Dark matter genesis thermal inflation first order phase transition decay flaton = saxino matter domination decay axinos radiation domination

59 Dark matter genesis thermal inflation first order phase transition axinos decay NLSP decay flaton = saxino matter domination decay radiation domination

60 Dark matter genesis thermal inflation first order phase transition decay flaton = saxino matter domination decay axinos NLSP decay radiation domination QCD phase transition axions

61 Dark matter genesis thermal inflation first order phase transition decay flaton = saxino matter domination decay axinos NLSP decay radiation domination QCD phase transition axions

62 Dark matter abundance Axion Axino

63 Dark matter abundance Axion Misalignment Axino ( f a Ω a GeV ) 1.2

64 Dark matter abundance Axion Misalignment ( f a Ω a GeV ) 1.2 Axino Flaton decay ( αã ) 2 ( mã ) ( ) 2 ( ) GeV 1 GeV Ωã GeV φ 0 T d

65 Dark matter abundance Axion Misalignment ( f a Ω a GeV ) 1.2 Axino Flaton decay ( αã ) 2 ( mã ) ( ) 2 ( ) GeV 1 GeV Ωã GeV Thermal NLSP decay ( mã ) ( GeV Ωã 10 1 GeV φ 0 ) 2 φ 0 T d

66 Dark matter abundance Flaton decays late Axion Misalignment ( µ T d 1 GeV TeV ( f a Ω a GeV ) 1.2 ) 2 ( ) GeV Axino Flaton decay ( αã ) 2 ( mã ) ( ) 2 ( ) GeV 1 GeV Ωã GeV Thermal NLSP decay ( mã ) ( GeV Ωã 10 1 GeV φ 0 ) 2 φ 0 φ 0 T d

67 Dark matter abundance Flaton decays late ( µ T d 1 GeV TeV ) 2 ( ) GeV φ 0 Axion Misalignment ( ) 1.2 f a Ω a GeV 1 for T d 1 GeV ( ) 2 Td for T d 1 GeV 1 GeV Axino Flaton decay ( αã ) 2 ( mã ) ( ) 2 ( ) GeV 1 GeV Ωã GeV Thermal NLSP decay ( mã ) ( GeV Ωã 10 1 GeV φ 0 ) 2 φ 0 T d

68 Dark matter abundance Flaton decays late ( µ T d 1 GeV TeV ) 2 ( ) GeV φ 0 Axion Misalignment ( ) 1.2 f a Ω a GeV 1 for T d 1 GeV ( ) 2 Td for T d 1 GeV 1 GeV Axino Flaton decay ( αã ) 2 ( mã ) ( ) 2 ( ) GeV 1 GeV Ωã GeV φ 0 T d Thermal NLSP decay ( mã ) ( ) 2 GeV Ωã 10 1 GeV φ 0 1 for T d m N ( ) 7 7 7Td for T d m N 7 m N

69 Dark matter composition Ω f a = GeV mã = 1 GeV axions 10 1 flaton axinos NLSP axinos µ GeV

70 Axino LHC signal NLSPs produced by the LHC decay to axinos plus Standard Model particles LHC NLSP axino SM

71 Axino LHC signal NLSPs produced by the LHC decay to axinos plus Standard Model particles LHC NLSP 1 km axino SM with a decay length ( 1 16πφ GeV Γ N ã mn 3 1 km m N and well constrained parameters φ GeV mã 1 GeV ) 3 ( φ GeV ) 2

72 Simple model MSSM neutrino masses MSSM µ-term drives m 2 φ < 0 W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ axion

73 Simple model MSSM neutrino masses MSSM µ-term drives m 2 φ < 0 W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ axion thermal inflation

74 Simple model MSSM neutrino masses MSSM µ-term drives m 2 φ < 0 W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ baryogenesis axion thermal inflation

75 Simple model MSSM neutrino masses MSSM µ-term drives m 2 φ < 0 W = λ u QH u ū + λ d QH d d + λe LH d ē λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ baryogenesis axion/axino dark matter thermal inflation

76 Rich cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl GeV ν R decay moduli, gravitinos,... matter/antimatter? disaster s 10 3 GeV 100 kev electroweak transition neutralino freeze out QCD transition nucleosynthesis matter/antimatter? neutralino dark matter? axion dark matter? light elements s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration yr time

77 Rich cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl GeV ν R decay moduli, gravitinos,... matter/antimatter? disaster s 10 3 GeV 100 kev thermal inflation LH u 0 φ decay QCD transition nucleosynthesis gravitational waves? matter/antimatter axino dark matter axion dark matter light elements s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration yr time

78 A Minimal Supersymmetric Cosmological Model Introduction Standard model of cosmology Moduli and gravitinos A Minimal Supersymmetric Cosmological Model MSSM MSCM Thermal inflation Baryogenesis Dark matter Summary Simple model Rich cosmology

Inflation from a SUSY Axion Model

Inflation from a SUSY Axion Model Masahiro Kawasaki (ICRR, Univ of Tokyo) with Naoya Kitajima (ICRR, Univ of Tokyo) Kazunori Nakayama (Univ of Tokyo) Based on papers MK, Kitajima, Nakayama, PRD 82, 123531