Inflaton Decay in Supergravity 30. May 2007 @Univ. of Tokyo - PowerPoint PPT Presentation

Inflaton Decay in Supergravity 30. May 2007 @Univ. of Tokyo Fuminobu Takahashi (DESY, Theory Group) M. Endo, K. Hamaguchi and F .T., hep-ph/0602061, 0605091 M. Kawasaki, F .T. and T. Yanagida, hep-ph/0603265, 0605091 M. Endo, M. Kawasaki, F .T. and T. Yanagida, hep-ph/0607170 M. Endo, F .T. and T. Yanagida, hep-ph/0701042

� ��� � ��฀� Thermal history after inflation Inflaton-decay reheats the universe. Severe constraints on T R come from thermally produced gravitinos. (assuming SUGRA) Reheating Reheating Reheating Reheating Reheating Reheating Reheating Reheating Reheating Reheating T R Inflaton- Radiation Std. BBC Inflation Oscillation Dominated Dominated e ± BBN Time

So far, couplings are introduced ad hoc by hand subject to the gravitino problem (due to thermally produced gravitinos) We have found inflaton decays via the top Yukawa coupling. gravitinos are non-thermally produced by inflaton decay.

So far, couplings are introduced ad hoc by hand subject to the gravitino problem (due to thermally produced gravitinos) We have found inflaton decays via the top Yukawa coupling. gravitinos are non-thermally produced by inflaton decay.

Inflaton Decay Processes: I. Gravitino pair production φ → 2 ψ 3 / 2 Kawasaki, F .T. and Yanagida, hep-ph/0603265, 0605297 Asaka, Nakamura and Yamaguchi, hep-ph/0604132 Dine, Kitano, Morisse and Shirman, hep-ph/0604140 Endo, Hamaguchi, FT, hep-ph/0605091 II. Spontaneous decay into any fields in superpotential (at tree level) Endo, Kawasaki, FT, Yanagida hep-ph/0607170 any gauge fields (at one-loop level) Endo, FT, Yanagida hep-ph/0701042

I. Gravitino Pair-Production Kawasaki, F .T. and Yanagida, hep-ph/0603265, 0605297 Asaka, Nakamura and Yamaguchi, hep-ph/0604132 Relevant interactions: − 1 8 ǫ µ νρσ ( G φ ∂ ρ φ + G z ∂ ρ z − h . c . ) ¯ e − 1 L = ψ µ γ ν ψ σ − 1 8 e G/ 2 ( G φ φ + G z z + h . c . ) ¯ ψ µ [ γ µ , γ ν ] ψ ν , φ : inflaton field G ≡ K + ln | W | 2 z : SUSY breaking field, w/ G z G z ≃ 3 Taking account of the mixings, G φ ∼ � φ � m 3 / 2 for m φ < m z m φ

Gravitino Pair Production Rate: � � φ � � 2 m 3 m 5 Γ 3 / 2 ≃ | G φ | 2 1 φ φ ≃ m 2 3 / 2 M 2 M 2 288 π 32 π M P P P for m φ < m z Endo, Hamaguchi and F .T., hep-ph/0602061 Nakamura and Yamaguchi, hep-ph/0602081 Gravitino pair production is effective especially for low-scale inflation models. Gravitino abundance is inversely proportional to the reheating temperature!

II. Spontaneous Decay Processes Inflaton couples to all the fields in the superpotential, through the SUGRA effects. visible (1) sector inflation sector (2) DSB sector (1) Lower limit on the reheating temperature (2) Decay into DSB sector produces gravitinos

Decay Rate through the Top Yukawa coupling: � � φ � � 2 m 3 3 φ 128 π 3 | Y t | 2 Γ T = , M 2 M P P Lower limit on the reheating temperature 10 19 : new(single);1TeV 12 : new(single);100TeV 10 10 18 : new(multi) 10 10 : hybrid 10 17 : smooth hyb. φ [GeV] 8 10 : chaotic (w/o Z ) 2 10 16 < > 10 15 10 14 6 10 4 2 10 10 13 0 10 -2 10 10 -4 10 10 12 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 15 10 16 10 17 m [GeV] φ

Decay Rate through the Top Yukawa coupling: � � φ � � 2 m 3 10 19 3 : new(single);1TeV φ 128 π 3 | Y t | 2 Γ T = , : new(single);100TeV 12 M 2 10 10 18 M P : new(multi) P 10 10 : hybrid Lower limit on the reheating temperature 10 17 : smooth hyb. φ [GeV] 8 10 : chaotic (w/o Z ) 2 10 16 10 19 : new(single);1TeV 12 : new(single);100TeV 10 < > 10 18 10 15 : new(multi) 10 10 : hybrid 10 17 : smooth hyb. φ [GeV] 8 10 : chaotic (w/o Z ) 2 10 14 10 16 6 10 < > 10 15 4 2 10 10 13 0 10 -2 10 10 14 10 -4 6 10 10 4 2 10 10 13 0 10 10 12 -2 10 10 -4 10 8 10 9 10 10 11 10 12 10 13 10 10 10 14 10 15 10 16 10 17 10 12 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 15 10 16 10 17 m [GeV] m [GeV] φ φ

(2) Decay into SUSY breaking sector Endo, F .T, Yanagida hep-ph/0701042 through Yukawa interactions at tree level through anomalies in SUGRA (at one-loop) ¯ g 2 D 2 � � 4( T R − 3 T G ) R † d 2 θ W α W α ∆ L = − (16 π ) 2 ∂ 2 � − T R 3 D 2 K + T R D 2 log det K | ′′ + h . c . R d R The rate of the decay into the hidden gauge sector is � � φ � � 2 m 3 Γ DSB = N ( h ) α 2 g 256 π 3 ( T ( h ) − T ( h ) φ R ) 2 h G M 2 M P P

Conservative Constraints on the inflation models; 10 19 : new(single);1TeV D : new(single);100TeV C 10 18 : new(multi) : hybrid 10 17 : smooth hyb. φ [GeV] : chaotic (w/o Z ) 2 10 16 A: m = 1TeV; Bh = 1 < > 10 15 3/2 -3 B: m = 1TeV; Bh = 10 3/2 C: m = 100TeV 10 14 3/2 A D: m = 1GeV 3/2 B 10 13 10 12 10 8 10 9 10 11 10 12 10 13 10 10 10 14 10 15 10 16 10 17 m [GeV] φ

Solutions: (i) Postulate a symmetry on the inflaton. e.g.) chaotic inflation V = 1 2 m 2 φ 2 w/ φ ↔ − φ (ii) AMSB, GMSB cosmological constraints are relaxed. (iii) late-time entropy production

Summary : We have discovered that gravitinos are generically produced from an inflaton decay.

Additional Slides

Gravitino Abundance: 2 Γ 3 / 2 3 T R Y 3 / 2 , ≃ 4 Γ total m φ 10 − 14 � g ∗ � − 1 � − 1 2 � T R ∼ 10 6 GeV 200 � 2 � � � φ � � 2 m φ × 10 15 GeV 10 10 GeV Γ total ∼ T 2 Note: R M P

Gravitino Abundance Y 3/2 thermal non-thermal T R

Potential minimization V = e G � G i G i − 3 � Differentiating V w.r.t. φ G φ ∇ φ G φ + G z ∇ φ G z + G φ = 0 ∇ φ G φ ∼ W φφ ∼ m φ ≫ 1 W m 3 / 2 ∇ φ G z ∼ W φ W z W ∼ � φ � W G φ ∼ � φ � m 3 / 2 m φ

Mass Matrix in SUGRA V = e G � G i G i − 3 � ∂ 2 V ∇ i G k ∇ j ∗ G k − R ij ∗ k ℓ ∗ G k G ℓ ∗ + g ij ∗ � ∂ϕ i ∂ϕ † j = e G � M 2 , = ij ∗ ∂ 2 V ∂ϕ i ∂ϕ j = e G � ∇ i G j + ∇ j G i + G k ∇ i ∇ j G k � M 2 M 2 , = ji = ij ∇ φ G φ ∼ W φφ ∼ m φ ≫ 1 W m 3 / 2 M 2 z � = 0 φ ¯ ∇ φ G z ∼ W φ W z W ∼ � φ � W

New inflation model Izawa and Yanagida ,`97 | φ | 2 + k 4 | φ | 4 , K ( φ , φ † ) = g v 2 φ − n + 1 φ n +1 . W ( φ ) = Successful inflation & density fluc. is realized if v = 4 × 10 − 7 (0 . 1 /g ) 1 / 2 for k � 0 . 03 n = 4 � φ � ≃ ( v 2 /g ) 1 /n m φ ≃ nv 2 / � φ �

Chaotic Inflation Kawasaki, Yamaguchi and Yanagida ,`00 2 ( φ + φ † ) 2 + · · · K ( φ + φ † ) = c ( φ + φ † ) + 1 W = m φψ m = 2 × 10 13 GeV Normalization: δ K = 1 Note: 2 κ ( φ + φ † ) zz + h . c . is allowed if z is a singlet.

Hybrid Inflation Models in supergravity W ( φ , ψ , ˜ ψ ) = φ ( µ 2 − λ ˜ ψψ ) , R-charge: φ (+2) , ψ ˜ ψ (0) w/ minimal Kahler U(1) gauge: φ (0) , ψ (1) , ˜ ψ ( − 1) √ � ψ � = � ˜ flat potential ψ � = 0 For | φ | ≫ µ/ λ Global minimum is located at � φ � = 0 √ � ψ � = � ˜ ψ � = µ/ λ φ Scalar spectral index: ψ n s ≃ 0 . 98 − 1 . 0

Smooth Hybrid Inflation Models � � µ 2 − ( ˜ ψψ ) n W ( φ , ψ , ˜ ψ ) = φ . M 2 n − 2 Global minimum is located at � φ � = 0 � ψ � = � ˜ ψ � = ( µM n − 1 ) 1 /n The dynamics is similar to hyb. inflation, but is slightly smaller. n s n s ≃ 0 . 967 − 0 . 97