Inflaton decay in supergravity and the new gravitino problem

Transcription

1 Inflaton decay in supergravity and the new gravitino problem 10. December University of Tokyo Fuminobu Takahashi (Institute for the Physics and Mathematics of the Universe) Collaborators: Endo, Hamaguchi, Kawasaki, Yanagida

2 1. Introduction Inflation : a phase of the exponential expansion. solves the horizon and flatness problems. Slow-roll inflation explains the origin of the density fluctuations. V

3 Inflation is now strongly supported by observations such as WMAP. Power-law LCDM model fits the WMAP data quite well. How can we select the inflation model realized in nature out of the inflationary zoo?

4 One approach is to study the properties of the density perturbations: scalar spectral index, scalar-to-tensor ratio, isocurvature perturbations, non- Gaussianities, etc.. Another is to check whether consistent thermal history of the universe can be realized after inflation.

5 Thermal history after inflation Inflaton-decay reheats the universe. Reheating contains information on the inflaton. Reheating Inflation Inflaton- Oscillation Dominated TR Radiation Dominated e ± Std. BBC BBN Time

6 Gravitino the superpartner of the graviton. It becomes massive by eating the goldstino when the local SUSY is spontaneously broken. (super-higgs mechanism) Interactions are very weak, and suppressed by M p or F m 3/2 M P long lifetime!

7 Gravitino Problem: Weinberg 82, Krauss 83 (from thermal scatterings) For high TR, too many gravitinos are thermally produced, leading to cosmological difficulties. Gravitino abundance (from thermal scattering) Moroi, Murayama, Yamaguchi 93, Bolz, Brandenburg, Buchmueller 01; Pradler, Steffen 06 Y 3/ ( TR GeV ) Upper bounds on T R

8 The reheating process itself has not been intensively studied! Couplings were introduced ad hoc by hand. Decay into unwanted relics such as the gravitinos was neglected without definite grounds. The reheating was constrained only by the gravitino problem (from thermal processes). It was far from satisfactory...

9 The reheating process itself has not been intensively studied! Couplings were introduced ad hoc by hand. Reheating:...Because the nature of the inflaton is not known, this process is still poorly understood... [from Wikipedia] Decay into unwanted relics such as the gravitinos was neglected without definite grounds. The reheating was constrained only by the gravitino problem (from thermal processes). It was far from satisfactory...

10 The reheating process itself has not been intensively studied! Couplings were introduced ad hoc by hand. Decay into unwanted relics such as the gravitinos was neglected without definite grounds. The reheating was constrained only by the gravitino problem (from thermal processes). It was far from satisfactory...

11 We have found gravitinos are non-thermally produced by inflaton decay. inflaton decays into the visible sector via the top Yukawa coupling and SU(3)c gauge interactions. Good : reheating is naturally induced. Bad(?) : new gravitino problem!

12 Plan of Talk 1. Introduction 2. Gravitino Pair-Production 3. Spontaneous Decay 4. Cosmological Constraints 5. Conclusions

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

14 Gravitino Production: (1) Gravitino pair production (direct) : (induced by the mixing between and ) (2) Anomaly-induced decay (indirect) : (decay into the hidden gauge sector) φ z SUSY breaking scale inflaton mass m (1) pair production (2) Anomaly-induced decay

15 2. Gravitino Pair-Production

16 Gravitino Pair-Production Relevant interactions: Kawasaki, F.T. and Yanagida, hep-ph/ , Asaka, Nakamura and Yamaguchi, hep-ph/ e 1 L = 1 8 ɛµνρσ (G φ ρ φ + G z ρ z h.c.) ψ µ γ ν ψ σ ^ ^ 1 8 eg/2 (G φ φ + G z z + h.c.) ψ µ [γ µ, γ ν ] ψ ν, φ : inflaton field z : SUSY breaking field, w/ G z G z 3 G K + ln W 2 Taking account of the mixings, G φ φ m 3/2 m φ for m φ < m z

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

18 Gravitino Abundance: Y 3/2 2 Γ 3/2 3 Γ total ( g 200 T R m φ, ) 1 2 ( TR 10 6 GeV ) 1 ( φ GeV ) 2 ( m φ GeV ) 2 Note: Γ total T 2 R M P

19 Gravitino Abundance Y 3/2 non-thermal thermal TR

20 3. Spontaneous Decay

21 Inflaton couples to any matter fields in the superpotential, and to any gauge sectors through the SUGRA effects. inflation sector φ 0 (1) anomaly-induced (2) tree-level & anomaly-induced DSB sector visible sector (1) Decay into DSB sector produces gravitinos (2) Lower limit on the reheating temperature

22 Anomaly-induced decay cf. anomaly-mediated SUSY breaking: The SW anomaly mediates the effects of the SUSY breaking to the visible sector. F Φ λ λ Φ : scalar auxiliary field in supergravity multiplet. m λ = g2 16π 2 b 0m 3/2

23 In a similar way, the anomaly couples the inflaton to any gauge sectors! φ φ x b µ Φ g g,, g g g 2 L = 64π 2 X G φ(f mn F mn if mn F mn ) X G = (T G T R )K φ + 2T R (log det K d R),φ, R g2 32π 2 X Gm φ φ λλ + h.c., Γ (anomaly) N gα 2 256π 3 X G 2 m 3 φ,

24 Decay into SUSY breaking sector (through Yukawa interactions at tree level) Endo, F.T, Yanagida hep-ph/ through anomalies in SUGRA (at one-loop) Γ DSB = N g (h) αh 2 ( ) 2 (h) (T 256π3 G T (h) φ m 3 R )2 φ M P M 2 P ψ µ φ φ x b µ Φ The gravitinos are produced from the hidden hadron decay.

25 Summary on the gravitino production rates: 1 32π ( φ M P ) 2 m 3 φ M 2 P, for m φ < Λ Γ 3/2 α 2 256π 3 ( φ M P ) 2 m 3 φ M 2 P, for m φ > Λ

26 4-1. Cosmological Constraints (gravitino production)

27 Conservative Constraints on the inflation models; < φ > [GeV] A C D B : new(single);1tev : new(single);100tev : new(multi) : hybrid : smooth hyb. : chaotic (w/o Z ) A: m 3/2= 1TeV; Bh = 1 B: m 3/2 = 1TeV; Bh = 10 C: m 3/2 = 100TeV D: m = 1GeV 3/ m [GeV] φ

28 Solutions: (i) Postulate a symmetry on the inflaton. e.g.) chaotic inflation V = 1 2 m2 φ 2 w/ φ φ (ii) AMSB, GMSB cosmological constraints are relaxed. (iii) late-time entropy production (iv) conformal sequestering

29 5. Conclusion We have discovered that the inflaton naturally decays into both the visible and SUSY breaking sectors. (1) New gravitino problem: non-thermal production of the gravitinos (2) Lower bound on the reheating temperature We obtained severe constraints on the inflation models and the SUSY breaking scenarios.

30 Additional Slides

31 Potential minimization Differentiating V w.r.t. φ V = e G ( G i G i 3 ) G φ φ G φ + G z φ G z + G φ = 0 φ G φ W φφ W m φ m 3/2 1 φ G z W φ W W z W φ G φ φ m 3/2 m φ

32 Mass Matrix in SUGRA V = e G ( G i G i 3 ) M 2 ij = 2 V ϕ i ϕ j = e G ( i G k j G k R ij kl G k G l ) + g ij, M 2 ij = M 2 ji = 2 V ϕ i ϕ j = e G ( i G j + j G i + G k i j G k ), φ G φ W φφ W m φ m 3/2 1 φ G z W φ W W z W φ M 2 φ z 0

33 New inflation model K(φ, φ ) = φ 2 + k 4 φ 4, W (φ) = v 2 φ g n + 1 φn+1. Successful inflation & density fluc. is realized if v = (0.1/g) 1/2 Izawa and Yanagida,`97 k 0.03 for n = 4 φ (v 2 /g) 1/n m φ nv 2 / φ

34 Chaotic Inflation Kawasaki, Yamaguchi and Yanagida,`00 K(φ + φ ) = c (φ + φ ) (φ + φ ) 2 + W = mφψ Normalization: m = GeV Note: δk = 1 2 κ(φ + φ )zz + h.c. is allowed if z is a singlet.

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

36 Smooth Hybrid Inflation Models W (φ, ψ, ψ) = φ ( µ 2 ( ψψ) n Global minimum is located at φ = 0 ψ = ψ = (µm n 1 ) 1/n M 2n 2 The dynamics is similar to hyb. inflation, but is slightly smaller. n s ns ).