Yong Tang University of Tokyo KEK, Dec 4-7, 2018 K.Nakayama & - - PowerPoint PPT Presentation

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Yong Tang

University of Tokyo

KEK, Dec 4-7, 2018

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Stochastic Gravitational Waves from Particle Origin

K.Nakayama & Y.Tang, 1810.04975

Phys.Lett. B 788 (2019) 341

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Frequency of GW

2

10−17Hz

1042Hz

Planck scale Hubble scale

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Frequency of GW

3

10−17Hz

1042Hz

LIGO Planck scale Hubble scale

102

10−3

LISA

10−8

SKA

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Sources of GW

• Cosmological
• Phase transition
• Primordial tensor fluctualtion
• Spectator decay during inflation
• Astrophysical
• Binaries of black holes, neutron stars
• Steller collapse
• Asymmetric rotating neutron star

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Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Sources of GW

• Cosmological
• Phase transition
• Primordial tensor fluctualtion
• Spectator decay during inflation
• Inflaton decay
• Astrophysical
• Binaries of black holes, neutron stars
• Steller collapse
• Asymmetric rotating neutron star

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Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Cosmic GW Background

• GW from inflaton decay
• directly related to inflation mass
• an inevitable contribution
• very high frequency
• contribute to the dark radiation Neff

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(a) (b) (c)

δNeff ' ¯ x 1 ¯ x ⇥ ( 2.86 mt < TE 5.59 mµ < TE < mπ f0 = M 2π Tγ0 TR

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Energy fraction

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10- 10-9 10-6 10-3 100 103 106 109 10 1015 10-18 10-15 10- 10-9 10-6 10-3 100 10- 10-9 10-6 10-3 100 103 106 109 10 1015 10-18 10-15 10- 10-9 10-6 10-3 100 [ ] DECIGO aLIGO(O1) LIGO IB IIB

• IA: M = 0.5MP, Γ = 10−5MP,
• IB: M = 0.1MP, Γ = 10−5MP,
• IIA: M = 0.5MP, Γ = 10−10MP,
• IIB: M = 0.1MP, Γ = 10−10MP,

Ω(f) ≡ 1 ρc dρ d ln f ,

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Formalism

• Action
• σ: inflaton field, V: potential
• φ: scalar, ψ: fermion
• Tµν :EM tensor
• hµν :graviton

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S =

• d4x
• |g|

M 2

P

2 R + 1 2gµν∂µσ∂νσ − V (σ) + δL

• ,

√

δL ⊃ µϕσϕ†ϕ + yψσ ¯ ψψ,

• 1

1 2 3 4 5 0.0 0.5 1.0 1.5 /Mp V1/4( )/10 Inflation Region Oscillation

MP = 1/ p 8πG ' 2.44 ⇥ 1018 GeV

gµν = ¯ gµν + κhµν

δL ⊃ κ 2 hµνT µν

κ ≡ √ 16πG = √ 2/MP

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Decay Width

• leading order
• Gravitational decay

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Γ0(σ → ϕ† + ϕ) = M 16π µϕ M 2 1 − 4y2 1

2 ,

Γ0(σ → ¯ ψ + ψ) = y2

ψM

8π

• 1 − 4y2 3

2 .

(a) (b) (c)

• and y = m/M.

processes ar

e bosonic decay (σ → ϕ† + ϕ + h),

fermionic decay (σ → ¯ ψ + ψ + h),

dΓ1 Mdx =(µϕ/Mp)2 64π3 1 − 2x + y4 − 3y2 x ln ✓1 + α 1 − α ◆ + 1 − 8x2 − 4xy2 + 8x + 2y2 4xα−1

• ,

dΓ1 Mdx = y2

ψ (M/Mp)2

64π3 " 2 ⇥ 1 + x2 y2 + 2

• + x
• −4y4 + 4y2 − 3
• + y4 − 3y2⇤

x ln ✓1 + α 1 − α ◆ +1 + 12x3 + 2x2 4y2 − 5

• + 4xy2 + 2y2

2xα−1 #

α = s 1 − 4y2 1 − 2x x = E M

M m

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Spectrum shape

• x = E/M

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s=0 s=1/2

10-7 10-6 10-5 10-4 10-3 10-2 10-1 0.055 0.060 0.065 0.070 x Γ1 Γ1 m=0.1M

dΓ1 dE ∝ 1 E when E → 0

Infrared behavior

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Energy fraction

• the energy that goes into graviton

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¯ x ≡ E M = Γ1 Γ Z 1/2

Λ/M

xdΓ1 Γ1dxdx, Γ = Γ0 + Γ1

s=0 s=1/2

10-2 10-1 100 10-6 10-5 10-4 10-3 10-2 M/MP x =0.1M,Λ=10-7M

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Dark Radiation

• Graviton will contribute to radiation component
• 12

δNeff ' ¯ x 1 ¯ x ⇥ ( 2.86 mt < TE 5.59 mµ < TE < mπ

δNeff

δNeff ≃ 4gs(TE) 7 gs(Tν) gs(TE) 4/3 ¯ x 1 − ¯ x,

gs(T):degree of freedom for relativistic SM at temperature T Tν: neutrino decoupling temperature TE: equilibrium temperature of SM particles begin (TE = TR)

For M ' MP , ¯ x ' 0.01. Future CMB may probe δNeff ' 0.03

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Spectrum of GW at Present

• The differential fraction of energy
• Term in the bracket is constant
• and

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Ω(f) ≡ 1 ρc dρ d ln f = ργ ρc  1 ργ E0dn d ln E0

• 1

ργ Edn d ln E '  2 gs(TR) 1/3 Γ1/Γ 1 ¯ x x2dΓ1 Γ1dx .

ργ/ρc = 5.38 × 10−5

E ' 2πf ⇥ TR/Tγ0, Tγ0 = 2.73 K = 8.6 ⇥ 10−5eV

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Spectrum of GW

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10- 10-9 10-6 10-3 100 103 106 109 10 1015 10-18 10-15 10- 10-9 10-6 10-3 100 10- 10-9 10-6 10-3 100 103 106 109 10 1015 10-18 10-15 10- 10-9 10-6 10-3 100 [ ] DECIGO aLIGO(O1) LIGO IB IIB

• IA: M = 0.5MP, Γ = 10−5MP,
• IB: M = 0.1MP, Γ = 10−5MP,
• IIA: M = 0.5MP, Γ = 10−10MP,
• IIB: M = 0.1MP, Γ = 10−10MP,

Ω(f) ≡ 1 ρc dρ d ln f ,

Akutsu et al, 0803.4094(PRL) at 100MHz

Ω . 1.2 × 1024

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Summary

• We consider the gravitational wave(GW) which

is directly from inflaton decay.

• GW will contribute to dark radiation Neff. If

inflaton is heavy ~Mp, maybe large enough to be probed by future CMB experiments.

• Such GW is in the very high-frequency range,

similar to CMB(~200GHz), requiring new technology.

• If from other particles’ decay during inflation,

GW may be in the detectable range, for instance

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Senatore, Silverstein and Zaldarriaga, 1109.0542

Yong TANG(U.Tokyo) Gravitational Waves from Particle Origin KEK

Thanks for your attention!

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10- 10-9 10-6 10-3 100 103 106 109 10 1015 10-18 10-15 10- 10-9 10-6 10-3 100 10- 10-9 10-6 10-3 100 103 106 109 10 1015 10-18 10-15 10- 10-9 10-6 10-3 100 [ ] DECIGO aLIGO(O1) LIGO IB IIB