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 2018.10.13

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

 a candidate for cold dark matter 1. Motivations  a candidate for cold dark matter Credit: http://www.esa.int/Planck

 a candidate for cold dark matter 1. Motivations  a candidate for cold dark matter  providing seeds for supermassive BHs Credit: 1211.2816

 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, 061101 PBH merger rate LIGO 𝑀~10 𝑀 ⨀ 𝑓 PBH

2. Constraints on the abundance of PBHs microlensing of stars femtolensing of γ-ray burst effects on CMB 1612.05644 1612.07264 extragalactic γ-rays Credit: 1701.02151

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

 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) 031301; J Liu, ZKG, RG Cai, G Shiu, in preparation； L Liu, J Liu, ZKG, RG Cai, in preparation

 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

new physics? power spectrum of primordial curvature perturbations 𝑘 PBH Credit: 1502.02114

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

hybrid-type inflation Credit: 1801.05235

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

𝑉(𝜙) 𝜙 𝜙 PBH 𝜙 ∗ a double inflection point inflationary model T.J. Gao, ZKG, PRD 98 (2018) 063526 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 − 1 2 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 )

 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

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