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

Thermal Gravitational Contribution to Dark Matter Production Yong Tang University of Tokyo KEK-PH, 2018 YL. Wu & Y. Tang , 1708.05138, 1604.04701 Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 1

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DM Scenarios Gravity SM DM Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 3

DM Scenarios Gravity SM DM New Interaction Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 4

DM Scenarios Gravity SM DM New Interaction Weakly Interacting Massive Particle • Mass around ~100GeV • Coupling ~ 0.5 • Correct relic abundance Ω ~0.3 • Searches for CDM • Collider qq > XXj Indirect detection Collider search • Direct Xq > Xq • Indirect XX > qq • Theoretically interesting Direct detection Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 5

DM Scenarios Gravity SM DM New Interaction 10 9 GeV 10 − 22 eV 10GeV 10 38 GeV 100TeV 10keV Primordial black hole Weakly Interacting Axion like scalar Sterile Neutrino WIMPZILLA Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 6

What if only Gravity? Gravity SM DM • 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 7

What if only Gravity? Gravity SM DM Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 8

Gravitational Contributions • Non-Thermal ( well-studied ) e.g. Ema, Jinno, Mukaida&Nakayama, 1502.02475,1604.08898 and refs. therein • Expansion of cosmic background • QFT in curved spacetime n X ∝ H 3 • Vacuum Fluctuation m X ∝ H • Bogoliubov transformation • Thermal scattering ( ) T > H or m φ • EFT for E<<M p L int = κ 2 h µ ν T µ ν , 1 √ Wu&Tang , 1604.04701, 1708.05138 32 π G ∼ κ = M P Gary,Sandora,Sloth&Palessandro ,1511.03278,1709.09688 Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 9

EFT in Einstein’s Gravity • Einstein-Hilbert action  � Z 1 L = √− g L d 4 x , S = 16 π GR + L m • EFT for E<<M p Justified after inflation L int = κ 2 h µ ν T µ ν , Energy-Momentum Tensor T µ ν = − ⌘ µ ν @ α S † @ α S + ⌘ µ ν m 2 S S † S + @ µ S † @ ν S + @ ν S † @ µ S, S @ F − m F FF � + 1 2 Fi � µ @ ν F + 1 T µ ν = − ⌘ µ ν � Fi/ 2 Fi � ν @ µ F F 4 @ ν � Fi � µ F � , + 1 2 ⌘ µ ν @ α � Fi � α F � − 1 4 @ µ � Fi � ν F � − 1 V V µ V ν � , ✓ 1 ◆ 4 F αβ F αβ − 1 T µ ν = ⌘ µ ν 2 m 2 V V α V α − � F µ α F να − m 2 V =1 Non-minimal coupling T µ ν 4 ⌘ µ ν F αβ F αβ − F µ α F να . γ ζ S † SR → 2 ζ ( ∂ µ ∂ ν − η µ ν ∂ α ∂ α ) S † S √ Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 10

Annihilation Processes • Boltzmann Equation � � a 3 n n + 3 Hn ≡ d = C col ˙ a 3 dt • Reduced to ✓ √ s � a 3 n � = g 2 T ◆ d Z ds σ √ s ( s − 4 m 2 ) K 1 , a 3 dt 32 π 4 T • The core Massless limit σ ∝ κ 4 s  4 | ~ p f | Wu&Tang 1604.04701 � = p i | A 32 ⇡ s ( Sg 2 i ) | ~ p p | ~ p i | = s 2 / 4 − m 2 , | ~ p f | = s 2 / 4 − M 2 Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 11

Various Contributions • Scalar Wu&Tang 1708.05138 A ( S → S ) =7 m 4 M 4 − m 2 M 2 m 2 + M 2 � � , 30 s 2 30 s + s 2 + 1 s m 4 + 4 m 2 M 2 + M 4 � m 2 + M 2 � � � + 240 , 40 120 A ( F → S ) = − 7 m 4 M 4 − m 2 M 2 ( M 2 − 4 m 2 ) 15 s 2 60 s 240(4 M 2 − m 2 ) + s 2 + 1 s 2 M 4 + 3 m 2 M 2 − 3 m 4 � � 480 , − 60 A ( V → S ) =101 m 4 M 4 − m 2 M 2 11 M 2 + m 2 � � 30 s 2 10 s + s 2 1 − 7 s 19 M 4 + 76 m 2 M 2 + 49 m 4 � m 2 + M 2 � � � + 80 , 120 120 A ( � → S ) = 1 s − 4 M 2 � 2 , � 120 Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 12

Various Contributions • Fermion Wu&Tang 1708.05138 A ( F ! F ) =14 m 4 M 4 + m 2 M 2 m 2 + M 2 � � , 15 s 2 30 s + s 2 1 s 8 m 4 � 3 m 2 M 2 + 8 M 4 � m 2 + M 2 � � � 160 , � � 120 120 A ( V ! F ) = � 101 m 4 M 4 + m 2 M 2 44 M 2 � m 2 � � 15 s 2 20 s + 13 s 2 � 1 s 7 M 2 + 52 m 2 � 19 M 4 � 19 m 2 M 2 � 26 m 4 � � � 480 , � 60 240 A ( γ ! F ) = 1 � s � 4 M 2 � (3 s + 8 M 2 ) , 120 • Vector A ( V ! V ) =2983 m 4 M 4 � 293 m 2 M 2 m 2 + M 2 � � , 30 s 2 10 s + 29 s 2 1 � 37 s 257 m 4 + 1188 m 2 M 2 + 257 M 4 � m 2 + M 2 � � � + 240 , 120 40 A ( γ ! V ) = 13 s � 4 M 2 � 2 , � 120 A ( γ ! γ ) = s 2 10 . Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 13

Parameter Space • Dark Matter X , 10 16 scalar Ω X = 0 . 258 fermion • Below DM m X, ↑Ω X 10 15 vector power-law; 
 T max [ GeV ] Above, log ↓Ω X 10 14 m X = T max • Similar for diff 
 10 13 spins. 10 12 Wu&Tang 1708.05138 10 4 10 6 10 8 10 10 10 12 10 14 10 16 m X [ GeV ] Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 14

Effects of Inflation • The temperature after inflation is determined by the reheating process, usually the decay of the inflaton. φ + 3 H ˙ ¨ φ + Ŵ φ ˙ φ + V ′ ( φ ) = 0 , V ( φ ) = 1 2 m 2 φ φ 2 ∗ = φ ≃ T R = � Ŵ φ M P maybe T R > m φ • Another important effect 
 is from inflaton annihilation. . reheating Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 15

Annihilation from Inflaton • The energy density during 
 φ X inflation is much lower than 
 Planck scale φ X  4 | ~ p f | � = p i | A 32 ⇡ s ( Sg 2 i ) | ~ M = M X m = m φ A = 1 • Scalar 2(1 − 6 ζ ) m 2 + M 2 ⇤ 2 ⇥ 32 • Fermion 1 helicity suppression 16 M 2 � m 2 − M 2 � • Vector 1 4 m 4 − 4 m 2 M 2 + 3 M 4 � � 32 • Massless vector 0 Wu&Tang 1708.05138 Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 16

Parameter Space • For massive scalar and vector = � ≃ � Ŵ φ � 1 / 2 Y X ≃ H ∗ T R ≃ m φ M 2 M P M P P • Fermion is suppressed 
 by a factor M 2 f /m 2 φ • Production from inflaton 
 annihilation could be 
 dominant Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 17

Possible Signatures • If stable, no signal in Direct/Indirect/Collider… • If unstable, decay products can be shown as anomalies in astrophysical observables Wu&Tang 1604.04701 Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 18

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. Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 19

Thanks for your attention. Yong TANG(U.Tokyo) Thermal Gravitational Contribution to DM KEK-PH 20