1. On the origin of primordial black holes
Zong-Kuan Guo
引力与宇宙学研讨会（大同）

2. Inflation
CMB
1st WAMP
Planck 2013
SNe
GWs
1982
1998
2003
2013
2016

3. 1. Motivations
 a candidate for cold dark matter [ ]
 to provide seeds for supermassive BHs [ , ]
 to provide seeds for cosmic structures [ ]
 to account for LIGO events [astro-ph/ , ]
2. Constraints on the PBH abundance [ ]
3. Discriminating PBHs from astrophysical BHs [ , ]
4. The origin of primordial balk holes
1) from early universe phase transition
 Q-balls [ ]
 vacuum bubbles [hep-ph/ , , ]
2) from preheating after inflation
 preheating [hep-ph/ ]
 tachyonic preheating [hep-ph/ ]
 oscillons [ ]
3) from large perturbations on small scales produced during inflation

4. from large perturbations on small scales produced during inflation
 multiple-field inflation [astro-ph/ , ]
 single-field inflation with an inflection point [ , ]
critical Higgs inflation [ , , ]
axion inflation [ , ]
supergravity [ ]
 a scalar field non-minimally coupled to gravity [ , ]
 the growth of perturbations on super-Hubble scales [ ]
 particle production during inflation [ , ]
 a contracting universe [ ]
 quantum diffusion during inflation [ , , ]

5. Credit: arXiv:
microlensing of stars
femtolensing of
γ-ray burst
effects on CMB
extragalactic γ-rays

6. 1/(𝑎𝐻) 1/𝑘 ln 𝑎 ∗ ln 𝑎 𝑒 ln 𝑎 eq 𝑀=𝛾 4𝜋 3 𝜌 𝐻 −3 =𝛾4𝜋 𝑀 pl 2 𝐻 −1
𝛽 𝑀 = 𝛿 𝑐 ∞ 𝑑𝛿 2𝜋 𝜎 𝑒 − 𝛿 2 2 𝜎 2
1/𝑘
𝛽 𝑀, 𝑡 eq = 𝑎( 𝑡 eq ) 𝑎( 𝑡 PBH ) 𝛽 𝑀
Ω PBH ( 𝑡 eq )= 𝑑 ln 𝑀 𝛽(𝑀, 𝑡 eq )
ln 𝑎 ∗
ln 𝑎 𝑒
ln 𝑎 eq
the threshold 𝛿 𝑐 =1/3 ?
the efficiency factor 𝛾~𝒪(1) ?
𝑓 PBH (𝑀)≡ Ω PBH (𝑀) Ω CDM

7. new physics?
𝑘 PBH

8. 𝑉(𝜙) 𝜙 𝜙 PBH 𝜙 ∗ 𝑢 𝑘 ′′ + 𝑘 2 − 𝑧 ′′ 𝑧 𝑢 𝑘 =0 50< 𝑁 ∗ <60
𝑢 𝑘 ′′ + 𝑘 2 − 𝑧 ′′ 𝑧 𝑢 𝑘 =0
𝑉(𝜙)
50< 𝑁 ∗ <60
𝒫 ℛ = 1 12 𝜋 2 𝑀 pl 6 𝑉 3 𝑉 𝜙 2
𝑁 𝜙 = 1 𝑀 pl 2 𝜙 𝑒 𝜙 𝑉 𝑉 𝜙 𝑑𝜙 𝜙
𝜙 PBH
𝜙 ∗
𝐴 𝑠 =(2.10±0.03)× 10 −9
𝑛 𝑠 =0.9649±0.0044
𝛼=−0.0065±0.0066
𝑟<0.07

9. 𝑉(𝜙) 𝜙 𝜙 PBH 𝜙 ∗ T.J. Gao, ZKG, arXiv:1806.09320
𝑉= 𝑒 𝐾 [ 𝐷 𝑖 𝑊 𝐾 −1 𝑖 𝑗 (𝐷 𝑗 𝑊) ∗ −3 |𝑊| 2 ]
𝐷 𝑖 𝑊= 𝜕 𝑖 𝑊+ 𝜕 𝑖 𝐾 𝑊
𝐾 𝑖 𝑗 = 𝜕 2 𝐾 𝜕 Φ 𝑖 𝜕 Φ 𝑗 𝜙
𝜙 PBH
𝜙 ∗
𝐾=𝑖𝑐 Φ− Φ − Φ− Φ 2 − 𝜁 4 (Φ− Φ ) 4
𝑊= 𝑎 0 (1+ 𝑎 1 𝑒 − 𝑏 1 Φ + 𝑎 2 𝑒 − 𝑏 2 Φ + 𝑎 3 𝑒 − 𝑏 3 Φ )

12. Thanks for your attention!

13. 不忘初心，继续前行