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

Inflaton Decay in Supergravity

Fuminobu Takahashi

(DESY, Theory Group)

• 30. May 2007

@Univ. of Tokyo

• 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

Inflaton-decay reheats the universe. Severe constraints on TR come from thermally produced gravitinos.

Inflation BBN

• Std. BBC

Inflaton- Oscillation Dominated

Radiation Dominated

• ฀

e±

Reheating Reheating Reheating Reheating Reheating Reheating Reheating Reheating Reheating Reheating

• Time

T

R

(assuming SUGRA)

Thermal history after inflation

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
• II. Spontaneous decay into

any fields in superpotential (at tree level) any gauge fields (at one-loop level)

φ → 2ψ3/2

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 Endo, Kawasaki, FT, Yanagida hep-ph/0607170 Endo, FT, Yanagida hep-ph/0701042

Relevant interactions:

e−1L = −1 8ǫµνρσ (Gφ∂ρφ + Gz∂ρz − h.c.) ¯ ψµγνψσ −1 8eG/2 (Gφφ + Gzz + h.c.) ¯ ψµ [γµ, γν] ψν,

G ≡ K + ln |W|2

φ : inflaton field

Kawasaki, F .T. and Yanagida, hep-ph/0603265, 0605297 Asaka, Nakamura and Yamaguchi, hep-ph/0604132

z : SUSY breaking field, w/ GzGz ≃ 3

• I. Gravitino Pair-Production

Gφ ∼ φ m3/2 mφ

for mφ < mz Taking account of the mixings,

Γ3/2 ≃ |Gφ|2 288π m5

φ

m2

3/2M 2 P

≃ 1 32π φ MP 2 m3

φ

M 2

P

Gravitino Pair Production Rate:

Endo, Hamaguchi and F .T., hep-ph/0602061 Nakamura and Yamaguchi, hep-ph/0602081

for mφ < mz

Gravitino pair production is effective especially for low-scale inflation models. Gravitino abundance is inversely proportional to the reheating temperature!

Inflaton couples to all the fields in the superpotential, through the SUGRA effects.

(1) Lower limit on the reheating temperature (2) Decay into DSB sector produces gravitinos inflation sector visible sector DSB sector (1) (2)

• II. Spontaneous Decay Processes

Decay Rate through the Top Yukawa coupling: Lower limit on the reheating temperature

109 1011 1013 1015

m [GeV]

φ

108

1015 1018 1017 1016 1014 1013 1019

< >

φ [GeV]

1010 1012 1014 1016

1012

1017 : hybrid : smooth hyb. : new(single);1TeV : new(multi) : chaotic (w/o Z ) : new(single);100TeV

2

10

• 4

10

• 2 10

0 10 2 10 4

10

6

10

8

10

10

10

12

ΓT = 3 128π3 |Yt|2 φ MP 2 m3

φ

M 2

P

,

Decay Rate through the Top Yukawa coupling: Lower limit on the reheating temperature

109 1011 1013 1015

m [GeV]

φ

108

1015 1018 1017 1016 1014 1013 1019

< >

φ [GeV]

1010 1012 1014 1016

1012

1017 : hybrid : smooth hyb. : new(single);1TeV : new(multi) : chaotic (w/o Z ) : new(single);100TeV

2

10

• 4

10

• 2 10

0 10 2 10 4

10

6

10

8

10

10

10

12

ΓT = 3 128π3 |Yt|2 φ MP 2 m3

φ

M 2

P

,

109 1011 1013 1015

m [GeV]

φ

108

1015 1018 1017 1016 1014 1013 1019

< >

φ [GeV]

1010 1012 1014 1016

1012

1017 : hybrid : smooth hyb. : new(single);1TeV : new(multi) : chaotic (w/o Z ) : new(single);100TeV

2

10

• 4

10

• 2 10

0 10 2 10 4

10

6

10

8

10

10

10

12

through Yukawa interactions at tree level through anomalies in SUGRA (at one-loop)

(2) Decay into SUSY breaking sector

Endo, F .T, Yanagida hep-ph/0701042

∆L = − g2 (16π)2

• d2θ W αWα

¯ D2 ∂2

• 4(TR − 3TG)R†

−TR 3 D2K + TR dR D2 log det K|

′′

R

• + h.c.

ΓDSB = N (h)

g

α2

h

256π3 (T (h)

G

− T (h)

R )2

φ MP 2 m3

φ

M 2

P

The rate of the decay into the hidden gauge sector is

Constraints on the inflation models;

109 1011 1013 1015

m [GeV]

φ

108

1015 1018 1017 1016 1014 1013 1019

< >

φ [GeV]

1010 1012 1014 1016

1012

1017

A B C D

: hybrid : smooth hyb. : new(single);1TeV : new(multi) : chaotic (w/o Z ) : new(single);100TeV

2

A: m = 1TeV; Bh = 1 B: m = 1TeV; Bh = 10 C: m = 100TeV D: m = 1GeV

3/2 3/2

• 3

3/2 3/2

Conservative

Solutions:

(iii) late-time entropy production (i) Postulate a symmetry on the inflaton. e.g.) chaotic inflation w/

V = 1

2m2φ2

φ ↔ −φ

(ii) AMSB, GMSB cosmological constraints are relaxed.

Summary:

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

Additional Slides

Gravitino Abundance:

Y3/2 ≃ 2 Γ3/2 Γtotal 3 4 TR mφ , ∼ 10−14 g∗ 200 − 1

2

TR 106GeV −1 ×

• φ

1015GeV 2 mφ 1010GeV 2

Γtotal ∼ T 2

R

MP

Note:

Gravitino Abundance

TR Y3/2

thermal non-thermal

Potential minimization

Gφ∇φGφ + Gz∇φGz + Gφ = 0

V = eG GiGi − 3

• Differentiating V w.r.t. φ

∇φGφ ∼ Wφφ W ∼ mφ m3/2 ≫ 1 ∇φGz ∼ Wφ W Wz W ∼ φ

Gφ ∼ φ m3/2 mφ

Mass Matrix in SUGRA

M 2

ij∗

= ∂2V ∂ϕi∂ϕ†j = eG ∇iGk∇j∗Gk − Rij∗kℓ∗GkGℓ∗ + gij∗ , M 2

ij

= M 2

ji =

∂2V ∂ϕi∂ϕj = eG ∇iGj + ∇jGi + Gk∇i∇jGk

• ,

V = eG GiGi − 3

• ∇φGφ ∼ Wφφ

W ∼ mφ m3/2 ≫ 1 ∇φGz ∼ Wφ W Wz W ∼ φ

M 2

φ¯ z = 0

New inflation model

K(φ, φ†) = |φ|2 + k 4|φ|4, W(φ) = v2φ − g n + 1 φn+1.

Izawa and Yanagida ,`97

Successful inflation & density fluc. is realized if v = 4 × 10−7 (0.1/g)1/2

k 0.03

n = 4

for

φ ≃ (v2/g)1/n mφ ≃ nv2/ φ

Chaotic Inflation

Kawasaki, Yamaguchi and Yanagida ,`00

K(φ + φ†) = c (φ + φ†) + 1

2(φ + φ†)2 + · · ·

W = mφψ m = 2 × 1013 GeV

Normalization:

δK = 1 2κ(φ + φ†)zz + h.c.

Note: is allowed if z is a singlet.

Hybrid Inflation Models in supergravity

W(φ, ψ, ˜ ψ) = φ(µ2 − λ ˜ ψψ),

Global minimum is located at

φ = 0 ψ = ˜ ψ = µ/ √ λ

Scalar spectral index: w/ minimal Kahler

ns ≃ 0.98 − 1.0

φ(0), ψ(1), ˜ ψ(−1)

U(1) gauge: R-charge:

φ(+2), ψ ˜ ψ(0)

For |φ| ≫ µ/ √ λ

ψ = ˜ ψ = 0

flat potential

ψ φ

W(φ, ψ, ˜ ψ) = φ

• µ2 − ( ˜

ψψ)n M 2n−2

• .

Smooth Hybrid Inflation Models

The dynamics is similar to hyb. inflation, but is slightly smaller.

ns ns ≃ 0.967 − 0.97 ψ = ˜ ψ = (µM n−1)1/n φ = 0

Global minimum is located at