Yong Tang University of Tokyo KEK-PH, 2018 YL. Wu & Y. Tang , - - PowerPoint PPT Presentation

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Yong Tang

University of Tokyo

KEK-PH, 2018

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Thermal Gravitational Contribution to Dark Matter Production

YL.Wu & Y.Tang, 1708.05138, 1604.04701

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Evidence of Dark Matter

• Galactic Rotation Curve
• Gravitational Lensing
• Large Scale Structure
• CMB anisotropies,
• …

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All confirmed evidence indicates DM at least has gravitational interaction.

• n of

Millenium simulation"

ΩX ' 0.26

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

DM Scenarios

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SM

DM

Gravity

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

DM Scenarios

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SM

DM

Gravity New Interaction

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

DM Scenarios

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SM

DM

Gravity New Interaction

Weakly Interacting Massive Particle

• Mass around ~100GeV
• Coupling ~ 0.5
• Correct relic abundance Ω~0.3
• Searches for CDM
• Collider qq > XXj
• Direct Xq > Xq
• Indirect XX > qq
• Theoretically interesting

Direct detection

Indirect detection Collider search

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

DM Scenarios

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SM

DM

Gravity New Interaction 10−22eV

10GeV

100TeV

10keV

Sterile Neutrino

Axion like scalar

Weakly Interacting

WIMPZILLA

Primordial black hole

109GeV 1038GeV

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

What if only Gravity?

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SM

DM

Gravity

• Gravitational interaction is

very weak.

• One may wonder whether

DM can be produced.

• We shall show gravity can

be strong enough to play…

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

What if only Gravity?

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SM

DM

Gravity

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Gravitational Contributions

• Non-Thermal (well-studied)
• Expansion of cosmic background
• QFT in curved spacetime
• Vacuum Fluctuation
• Bogoliubov transformation
• Thermal scattering ( )
• EFT for E<<Mp

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Lint = κ 2 hµνT µν,

nX ∝ H3

Wu&Tang, 1604.04701, 1708.05138

Gary,Sandora,Sloth&Palessandro,1511.03278,1709.09688

e.g. Ema, Jinno, Mukaida&Nakayama, 1502.02475,1604.08898 and refs. therein

κ = √ 32πG ∼ 1 MP

mX ∝ H

T > H or mφ

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

EFT in Einstein’s Gravity

• Einstein-Hilbert action
• EFT for E<<Mp

Energy-Momentum Tensor

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T µν

S

= − ⌘µν@αS†@αS + ⌘µνm2

SS†S + @µS†@νS + @νS†@µS,

T µν

F

= − ⌘µν Fi/ @F − mF FF + 1 2Fiµ@νF + 1 2Fiν@µF + 1 2⌘µν@α FiαF − 1 4@µ FiνF − 1 4@ν FiµF , T µν

V

=⌘µν ✓1 4F αβFαβ − 1 2m2

V V αVα

◆ − F µαF να − m2

V V µV ν ,

T µν

γ

=1 4⌘µνF αβFαβ − F µαF να. √

L = √−g  1 16πGR + Lm

• S =

Z L d4x ,

Lint = κ 2 hµνT µν,

ζS†SR → 2ζ(∂µ∂ν − ηµν∂α∂α)S†S Non-minimal coupling Justified after inflation

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Annihilation Processes

• Boltzmann Equation
• Reduced to
• The core

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|~ pi| = p s2/4 − m2, |~ pf| = p s2/4 − M 2

= 4 32⇡s (Sg2

i )

|~ pf| |~ pi| A

d

• a3n
• a3dt

= g2T 32π4 Z ds σ √s(s − 4m2)K1 ✓√s T ◆ ,

˙ n + 3Hn ≡ d

• a3n
• a3dt

= Ccol

σ ∝ κ4s

Massless limit Wu&Tang 1604.04701

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Various Contributions

• Scalar

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A (S → S) =7m4M 4 30s2 − m2M 2 30s

• m2 + M 2

, + 1 40

• m4 + 4m2M 2 + M 4

+ s 120

• m2 + M 2

+ s2 240, A (F → S) = − 7m4M 4 15s2 − m2M 2 60s (M 2 − 4m2) + 1 60

• 2M 4 + 3m2M 2 − 3m4

− s 240(4M 2 − m2) + s2 480, A (V → S) =101m4M 4 30s2 − m2M 2 10s

• 11M 2 + m2

+ 1 120

• 19M 4 + 76m2M 2 + 49m4

− 7s 120

• m2 + M 2

+ s2 80, A ( → S) = 1 120

• s − 4M 22 ,

Wu&Tang 1708.05138

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Various Contributions

• Fermion
• Vector

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A (F ! F) =14m4M 4 15s2 + m2M 2 30s

• m2 + M 2

,

• 1

120

• 8m4 3m2M 2 + 8M 4
• s

120

• m2 + M 2

+ s2 160, A (V ! F) = 101m4M 4 15s2 + m2M 2 20s

• 44M 2 m2

1 60

• 19M 4 19m2M 2 26m4
• s

240

• 7M 2 + 52m2

+ 13s2 480 , A (γ ! F) = 1 120

• s 4M 2

(3s + 8M 2), A (V ! V ) =2983m4M 4 30s2 293m2M 2 10s

• m2 + M 2

, + 1 120

• 257m4 + 1188m2M 2 + 257M 4

37s 40

• m2 + M 2

+ 29s2 240 , A (γ ! V ) = 13 120

• s 4M 22 ,

A (γ ! γ) = s2 10.

Wu&Tang 1708.05138

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Parameter Space

• Dark Matter X,
• Below DM mX,

power-law;
 Above, log

• Similar for diff


spins.

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scalar fermion vector 104 106 108 1010 1012 1014 1016 1012 1013 1014 1015 1016 mX[GeV] Tmax[GeV]

mX=Tmax

↓ΩX ↑ΩX

ΩX = 0.258

Wu&Tang 1708.05138

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Effects of Inflation

• The temperature after inflation is determined by

the reheating process, usually the decay of the inflaton.

• Another important effect 


is from inflaton annihilation..

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¨ φ + 3H ˙ φ + Ŵφ ˙ φ + V ′(φ) = 0,

∗ = φ

≃ T R = ŴφM P

V (φ) = 1 2m2

φφ2 reheating

maybe TR > mφ

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Annihilation from Inflaton

• The energy density during 


inflation is much lower than
 Planck scale

• Scalar
• Fermion
• Vector
• Massless vector

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φ φ

1 16M 2 m2 − M 2

1 32

• 4m4 − 4m2M 2 + 3M 4

= 4 32⇡s (Sg2

i )

|~ pf| |~ pi| A

A = 1 32 ⇥ 2(1 − 6ζ)m2 + M 2⇤2

m = mφ

M = MX

X X

helicity suppression

Wu&Tang 1708.05138

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Parameter Space

• For massive scalar and vector
• Fermion is suppressed


by a factor

• Production from inflaton 


annihilation could be 
 dominant

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≃ =

Y X ≃ H∗ M2

P

T R ≃ mφ M P

Ŵφ

M P

1/2

M 2

f /m2 φ

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Possible Signatures

• If stable, no signal in Direct/Indirect/Collider…
• If unstable, decay products can be shown as

anomalies in astrophysical observables

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Wu&Tang 1604.04701

Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Summary

• Gravitational contributions to dark matter

production can be important for non-WIMP case

• We consider the contribution due to thermal SM

particles’ gravitational annihilation

• Inflation plays two important roles
• Reheating temperature
• Inflaton’s gravitational annihilation
• Possible astrophysical signatures if DM decay.

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Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH

Thanks for your attention.

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