On the origin of primordial black holes Zong-Kuan Guo 引力与宇宙学研讨会（大同） 2018.8.27

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

1. Motivations  a candidate for cold dark matter [1607.06077]  to provide seeds for supermassive BHs [1202.3848, 1712.01311]  to provide seeds for cosmic structures [1801.00672]  to account for LIGO events [astro-ph/9708060, 1603.08338] 2. Constraints on the PBH abundance [1701.02151] 3. Discriminating PBHs from astrophysical BHs [1806.05195, 1708.07380] 4. The origin of primordial balk holes 1) from early universe phase transition  Q-balls [1612.02529]  vacuum bubbles [hep-ph/9807343, 1710.02865, 1804.10059] 2) from preheating after inflation  preheating [hep-ph/0410247]  tachyonic preheating [hep-ph/0601108]  oscillons [1801.03321] 3) from large perturbations on small scales produced during inflation

from large perturbations on small scales produced during inflation  multiple-field inflation [astro-ph/9605094, 1501.07565]  single-field inflation with an inflection point [1702.03901, 1707.09578] critical Higgs inflation [1705.04861, 1706.05007,1805.02160] axion inflation [1704.03464, 1801.09050] supergravity [1806.09320]  a scalar field non-minimally coupled to gravity [1705.06225, 1712.09896]  the growth of perturbations on super-Hubble scales [1710.11196]  particle production during inflation [1511.08470, 1606.00206]  a contracting universe [1609.02556]  quantum diffusion during inflation [1707.00537, 1805.06731, 1801.09415]

Credit: arXiv:1701.02151 microlensing of stars femtolensing of γ-ray burst effects on CMB 1612.05644 1612.07264 extragalactic γ-rays

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

new physics? 𝑘 PBH

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

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 − 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 )

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