1. The origin of primordial black holes — a double inflection point inflationary model
Zong-Kuan Guo
第二届新疆理论物理前沿学术研讨会

2. 1. Motivations
2. Constraints on the abundance of PBHs
3. The origin of PBHs
4. Open questions

3.  a candidate for cold dark matter
1. Motivations
 a candidate for cold dark matter
Credit:

4.  a candidate for cold dark matter
1. Motivations
 a candidate for cold dark matter
 providing seeds for supermassive BHs
Credit:

5.  a candidate for cold dark matter
1. Motivations
 a candidate for cold dark matter
 providing seeds for supermassive BHs
 accounting for the LIGO events
Credit: PRL 117,
PBH merger rate
LIGO
𝑀~10 𝑀 ⨀
𝑓 PBH

9. 2. Constraints on the abundance of PBHs
microlensing of stars
femtolensing of
γ-ray burst
effects on CMB
extragalactic γ-rays
Credit:

10. 3. The origin of PBHs false vacuum vacuum vacuum false vacuum
 from early universe phase transition
𝑉(𝜙)
false vacuum
vacuum
vacuum
false vacuum

11.  from preheating after inflation
3. The origin of PBHs
 from early universe phase transition
 from preheating after inflation
J Liu, ZKG, RG Cai, G Shiu, PRL 120 (2018) ;
J Liu, ZKG, RG Cai, G Shiu, in preparation；
L Liu, J Liu, ZKG, RG Cai, in preparation

12.  from preheating after inflation
3. The origin of PBHs
 from early universe phase transition
 from preheating after inflation
 from large primordial perturbations on small scales
~7𝜎

13. new physics?
power spectrum of primordial curvature perturbations
𝑘 PBH
Credit:

14. 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

15. hybrid-type inflation
Credit:

16. 𝑉(𝜙) 𝜙 𝜙 PBH 𝜙 ∗ 𝒫 ℛ = 1 12 𝜋 2 𝑀 pl 6 𝑉 3 𝑉 𝜙 2 50< 𝑁 ∗ <60
𝑢 𝑘 ′′ + 𝑘 2 − 𝑧 ′′ 𝑧 𝑢 𝑘 =0
𝜙 PBH
𝜙 ∗
𝜖 0 = 1 𝐻 , 𝜖 𝑖+1 = 𝑑 ln | 𝜖 𝑖 | 𝑑𝑁
𝐴 𝑠 =(2.10±0.03)× 10 −9
𝑛 𝑠 =0.9649±0.0044
𝛼=−0.0065±0.0066
𝑟<0.07

17. 𝑉(𝜙) 𝜙 𝜙 PBH 𝜙 ∗ a double inflection point inflationary model
T.J. Gao, ZKG, PRD 98 (2018)
𝑉= 𝑒 𝐾 [ 𝐷 𝑖 𝑊 𝐾 −1 𝑖 𝑗 (𝐷 𝑗 𝑊) ∗ −3 |𝑊| 2 ]
𝑉(𝜙)
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 )

20.  The evolution of the mass function of PBHs
4. Open questions
 How to discriminate PBHs from astrophysical BHs
— 𝑡, 𝑥, 𝑚, 𝑄, 𝐽
 The evolution of the mass function of PBHs
 The effect on the cosmic large-scale structure formation

21. Thanks for your attention!