A Minimal Supersymmetric Cosmological Model

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/9603324 hep-ph/0406136 hep-ph/0703275 arxiv:0801.4197 arxiv:0807.3607

Standard model of cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl 10 11 GeV ν R decay matter/antimatter? 10 28 s 10 3 GeV 100 kev electroweak transition neutralino freeze out QCD transition nucleosynthesis matter/antimatter? neutralino dark matter? axion dark matter? light elements 10 13 s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration 10 10 yr time

Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains n s 10 12 to 10 15

Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s 10 12 to 10 15 H 2 (Ψ Ψ 1 ) 2

Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s 10 12 to 10 15 H 2 (Ψ Ψ 1 ) 2 m 2 susy (Ψ Ψ 0 ) 2 M Pl

Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s 10 12 to 10 15 n s 107 m 2 susy (Ψ Ψ 0 ) 2 M Pl

Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s 10 12 to 10 15 n s 107 m 2 susy (Ψ Ψ 0 ) 2 M Pl Moduli generated: H m susy

Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s 10 12 to 10 15 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

Moduli and gravitinos Moduli are cosmologically dangerous. Nucleosynthesis constrains In the early universe n s 10 12 to 10 15 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

Standard model of cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl 10 11 GeV ν R decay moduli, gravitinos,... matter/antimatter? disaster 10 28 s 10 3 GeV 100 kev electroweak transition neutralino freeze out QCD transition nucleosynthesis matter/antimatter? neutralino dark matter? axion dark matter? light elements 10 13 s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration 10 10 yr time

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

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?

Minimal Supersymmetric Cosmological Model W = λ u QH u ū + λ d QH d d + λe LH d ē + 1 2 λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ

Minimal Supersymmetric Cosmological Model MSSM W = λ u QH u ū + λ d QH d d + λe LH d ē + 1 2 λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ

Minimal Supersymmetric Cosmological Model MSSM neutrino masses W = λ u QH u ū + λ d QH d d + λe LH d ē + 1 2 λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ

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 + 1 2 λ ν (LH u ) 2 +λ µ φ 2 H u H d +λ χ φχ χ µ = λ µ φ 2 0

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 + 1 2 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

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 + 1 2 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

Thermal inflation V V 0 RADIATION DOMINATION φ 0 φ

Thermal inflation V V 0 THERMAL INFLATION φ 0 φ

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

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

Thermal inflation V V 0 MATTER DOMINATION φ 0 φ

Key properties of thermal inflation For φ 0 10 10 to 10 12 GeV

Key properties of thermal inflation For Large dilution φ 0 10 10 to 10 12 GeV 10 20 = pre-existing moduli sufficiently diluted

Key properties of thermal inflation For Large dilution φ 0 10 10 to 10 12 GeV 10 20 = pre-existing moduli sufficiently diluted Short duration N 10 = primordial perturbations from slow-roll inflation preserved on large scales Low energy scale V 1/4 0 10 6 to 10 7 GeV = moduli regenerated with sufficiently small abundance

Gravitational waves Ω GW 10 5 10 10 10 15 DECIGO INFLATION PREHEATING 10 20 10 25 10 30 PRIMORDIAL INFLATION 10 35 10 40 10 10 10 5 10 0 10 5 10 10 f Hz

Gravitational waves 10 5 Ω GW 10 10 10 15 DECIGO 10 20 10 25 10 30 10 35 PRIMORDIAL INFLATION THERMAL INFLATION INFLATION PREHEATING 10 40 10 10 10 5 10 0 10 5 10 10 f Hz

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

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

Reduction W = λ u QH u ū + λ d QH d d + λe LH d ē + 1 2 λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ

Reduction W = λ u QH u ū + λ d QH d d + λe LH d ē + 1 2 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 = ( 0 0 0 ) (, Q = h u ), H d = 0 0 0 d/ 2 0 0 ) ( hd 0 φ = φ, χ = 0, χ = 0 ), ē = ( e/ 2 ), d = ( d/ 2 0 0 )

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 [ 1 + 2 A νλ ν l 2 hu 2 1 2 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 2 2 + λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u + 1 2 λ dd 2 + 1 2 2 λ ee 2 + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d 2 + 1 2 g 2 ( h u 2 h d 2 l 2 + 1 2 d 2 + 1 2 e 2 ) 2

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 [ 1 + 2 A νλ ν l 2 hu 2 1 2 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 2 2 + λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u + 1 2 λ dd 2 + 1 2 2 λ ee 2 + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d 2 + 1 2 g 2 ( h u 2 h d 2 l 2 + 1 2 d 2 + 1 2 e 2 ) 2

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 [ 1 + 2 A νλ ν l 2 hu 2 1 2 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 2 2 + λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u + 1 2 λ dd 2 + 1 2 2 λ ee 2 + λ d h d d 2 + λ e h d e 2 + 2λ µ φh u h d 2 + 1 2 g 2 ( h u 2 h d 2 l 2 + 1 2 d 2 + 1 2 e 2 ) 2

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 [ 1 + 2 A νλ ν l 2 hu 2 1 2 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 2 2 + λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u + 1 2 λ dd 2 + 1 2 2 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 2 + 1 2 g 2 ( h u 2 h d 2 l 2 + 1 2 d 2 + 1 2 e 2 ) 2

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 [ 1 + 2 A νλ ν l 2 hu 2 1 2 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 2 2 + λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u + 1 2 λ dd 2 + 1 2 2 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 2 + 1 2 g 2 ( h u 2 h d 2 l 2 + 1 2 d 2 + 1 2 e 2 ) 2

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 [ 1 + 2 A νλ ν l 2 hu 2 1 2 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 2 2 + λ ν l 2 h u λ µ φ 2 2 h d + λ µ φ 2 h u + 1 2 λ dd 2 + 1 2 2 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 2 + 1 2 g 2 ( h u 2 h d 2 l 2 + 1 2 d 2 + 1 2 e 2 ) 2 d and e held at origin lh u returns with rotation h d forced out

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

Numerical simulation n L /n AD 0.15 0.1 0.05 0 0.05 0.1 0.15 mt 0 200 400 600 800 1000

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

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 0 10 9 GeV (10 2 ev m ν ) (mlhu TeV ) gives ( 10 12 ) ( ) 2 GeV µ T d 1 GeV TeV φ 0 n B s 10 10 ( nl /n AD 10 2 ) ( 10 12 ) 3 ( GeV 10 2 ev φ 0 m ν ) ( µ TeV ) 2 ( 10 1 α φ ) ( mlhu m φ (0) ) 2

Dark matter candidates Peccei-Quinn symmetry W = λ u QH u ū +λ d QH d d +λe LH d ē + 1 2 λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ

Dark matter candidates Peccei-Quinn symmetry DFSZ axion W = λ u QH u ū +λ d QH d d +λe LH d ē + 1 2 λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ

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 + 1 2 λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ

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 + 1 2 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 ( 10 6.2 10 6 12 ) GeV ev f a

Dark matter genesis thermal inflation

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

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

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

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

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

Dark matter abundance Axion Axino

Dark matter abundance Axion Misalignment Axino ( f a Ω a 3 10 12 GeV ) 1.2

Dark matter abundance Axion Misalignment ( f a Ω a 3 10 12 GeV ) 1.2 Axino Flaton decay ( αã ) 2 ( mã ) ( 3 10 12 ) 2 ( ) GeV 1 GeV Ωã 0.04 10 1 1 GeV φ 0 T d

Dark matter abundance Axion Misalignment ( f a Ω a 3 10 12 GeV ) 1.2 Axino Flaton decay ( αã ) 2 ( mã ) ( 3 10 12 ) 2 ( ) GeV 1 GeV Ωã 0.04 10 1 1 GeV Thermal NLSP decay ( mã ) ( 10 12 GeV Ωã 10 1 GeV φ 0 ) 2 φ 0 T d

Dark matter abundance Flaton decays late Axion Misalignment ( µ T d 1 GeV TeV ( f a Ω a 3 10 12 GeV ) 1.2 ) 2 ( 10 12 ) GeV Axino Flaton decay ( αã ) 2 ( mã ) ( 3 10 12 ) 2 ( ) GeV 1 GeV Ωã 0.04 10 1 1 GeV Thermal NLSP decay ( mã ) ( 10 12 GeV Ωã 10 1 GeV φ 0 ) 2 φ 0 φ 0 T d

Dark matter abundance Flaton decays late ( µ T d 1 GeV TeV ) 2 ( 10 12 ) GeV φ 0 Axion Misalignment ( ) 1.2 f a Ω a 3 10 12 GeV 1 for T d 1 GeV ( ) 2 Td for T d 1 GeV 1 GeV Axino Flaton decay ( αã ) 2 ( mã ) ( 3 10 12 ) 2 ( ) GeV 1 GeV Ωã 0.04 10 1 1 GeV Thermal NLSP decay ( mã ) ( 10 12 GeV Ωã 10 1 GeV φ 0 ) 2 φ 0 T d

Dark matter abundance Flaton decays late ( µ T d 1 GeV TeV ) 2 ( 10 12 ) GeV φ 0 Axion Misalignment ( ) 1.2 f a Ω a 3 10 12 GeV 1 for T d 1 GeV ( ) 2 Td for T d 1 GeV 1 GeV Axino Flaton decay ( αã ) 2 ( mã ) ( 3 10 12 ) 2 ( ) GeV 1 GeV Ωã 0.04 10 1 1 GeV φ 0 T d Thermal NLSP decay ( mã ) ( 10 12 ) 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

Dark matter composition 10 1 10 0 Ω f a = 10 12 GeV mã = 1 GeV axions 10 1 flaton axinos NLSP axinos 10 2 10 2 10 3 10 4 µ GeV

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

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 16πφ2 0 200 GeV Γ N ã mn 3 1 km m N and well constrained parameters φ 0 10 12 GeV mã 1 GeV ) 3 ( φ 0 10 12 GeV ) 2

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 + 1 2 λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ axion

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 + 1 2 λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ axion thermal inflation

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 + 1 2 λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ baryogenesis axion thermal inflation

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 + 1 2 λ ν (LH u ) 2 + λ µ φ 2 H u H d + λ χ φχ χ baryogenesis axion/axino dark matter thermal inflation

Rich cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl 10 11 GeV ν R decay moduli, gravitinos,... matter/antimatter? disaster 10 28 s 10 3 GeV 100 kev electroweak transition neutralino freeze out QCD transition nucleosynthesis matter/antimatter? neutralino dark matter? axion dark matter? light elements 10 13 s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration 10 10 yr time

Rich cosmology (density) 1/4 m Pl inflation density perturbations gravitational waves? t Pl 10 11 GeV ν R decay moduli, gravitinos,... matter/antimatter? disaster 10 28 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 10 13 s 10 min 10 K atom formation galaxy formation vacuum energy dominates microwave background galaxies acceleration 10 10 yr time

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