Primordial Black Holes from QCD axion walls
Shuailiang Ge(Peking University)
2307.08185 Shuailiang Ge
2309.01739 Shuailiang Ge, Jinhui Guo, and Jia Liu

December 5, 2023

Why we need QCD axion?
Strong CP problem: ℒQCD ⊃ θ̄2gs32π

G̃
2aμν

aGμν

(CP-violation term)θ̄ = θvac + arg det(YuYd)
SU(3)color vacuum topology

quark sector−10[theory: θ̄ ∈ (0, 2π)] vs. [experiments: θ̄ ≲ 10](neutron electric dipole moment)

Why θ̄ is so unnaturally small (Fine-tuning)?
strong CP problem
Shuailiang Ge (PKU)2

Solution: Peccei-Quinn (PQ) mechanism
Global symmetry U(1)PQ:
2gsΦ = ρ exp(ia/fa)

aaμν a2=>,[anomaly]
SU(3)
×U(1)
G̃GPQμν
color
2
fa 32π(Roberto Peccei)(Hellen Quinn)2gsaaμν aℒQCD ⊃ θ̄ +G̃Gμν
2f32π(a)θ̄ is absorbed into a:θ̄ + a/fa → a/fa , dynamical eld.
a is called axion.
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Axion Topological Defects
1. PQ symmetry spontaneous breaks:λ †2 2ℒϕ ⊃ − (Φ Φ − fa )4

Axion Strings

ϕ = ρ exp(ia/fa)

T ∼ fa ∼ 1012GeV(taken from Ringeval 1005.4842)

2. Non-perturbative e ects explicitly breaking PQ:
2 2Va ≃ ma fa [1 − cos(a/fa)]Axion domain walls

T ∼ 1 GeV
ff

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Axion Topological Defects(Chang, Hagmann & Sikivie,1998)(Vachaspati & Vilenkin,1984)

Computer Simulations
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Simulation of the string-wall network(SG, Jinhui Guo, Jia Liu,2023)

open walls bounded by strings

Closed domain wall

(NDW = 1)

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Simulation of the string-wall network(SG, Jinhui Guo, Jia Liu,open walls bounded by strings2023)

Closed domain wall

(NDW = 1)002⇡

0Shuailiang Ge (PKU)

Closed Domain wall07

Fate of closed domain walls?
>> Collapses and oscillates.
Energy released mainly in the form of free axions.
Nothing interesting.
>> Schwartzchild radius RS = 2GM.

If the wall radius R < Rs(R, t), a Black Hole is formed!
2M = 4πR ⋅ σ where σ is the domain wall surface energy (i.e., tension)
so the criterion becomes:(Widrow, 1989)(Vachaspati, 2017)(SG, 2019)

R > 1/(8πGσ)
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Di erent Scenarios of Axion Cosmology>> Pre-in ationary scenario: PQ symmetry breaks before in ation.
fa ≳ HI /2π

The formed strings will be blown away by in ation;
Axion eld gets homogenized;
No axion domains walls can form.

>> Post-in ationary scenario: PQ symmetry breaks after in ation.
fa ≲ HI /2π
String-wall network will form.
>> During-in ation scenario: PQ symmetry breaks during in ation.
String-wall network will form but re-enters horizon much later.
fa ∼ HI /2π9fl

fl

fl

fl

fl

fl

fl

fiff

Shuailiang Ge (PKU)

>> During-in ation scenario: PQ symmetry breaks during in ation.
String-wall network will form but re-enters horizon much later.

fa ∼ HI /2π :ne-tuning? NO!

This relation is not necessary

This scenario can be naturally realized if the PQ symmetry breaking
driven by in ation, for example:
see e.g.,(Keisuke Harigaya, Lian-Tao Wang, 2022),(Michele Redi, Andrea Tesi, 2022)

PQ symmetry breaks when

(Haipeng An, Chen Yang, 2023)

10
fl

fl

fl

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flfi

During-in ationary Scenario

During-in ationary Scenario

Ten: the temperature of re-entering horizon
Size of closed axion domain walls: R ∼ H

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Criterion for PBH formation
Numerical calculation:

Equation of motion:
Initial condition:

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Criterion for PBH formation
Criterion: R < Rs(R, t)(Vachaspati, 2017)(SG, 2019)

We get,Shuailiang Ge (PKU)13

Criterion for PBH formation~400 MeV

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Abundance(SG, Jinhui Guo, Jia Liu,2023)

open walls bounded by strings

Closed domain wall

(NDW = 1)

fraction of lattice cells occupied by a piece of wall.
total closed wall areaγ ≡ total DW area
The simulation results are independent of axion parameters or Ten
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PBH abundance

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PBH abundance
Intriguing astronomical implications:>> Anomalous microlensing events
observed by the OGLE collaboration.
(Mroz et al 2017; Niikura et al, 2019),>> Explain the Planet 9 in our solar
system if it is a PBH.
(Scholt and Unwin, 2020; Witten, 2020)

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PBH abundance

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PBH abundance

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PBH abundance

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Summary>> Closed walls naturally arise in the domain wall network.
>> Although the number density of closed walls is low, they
can lead to very interesting and observable results (PBHs).
>> The resultant PBHs may explain the OGLE microlensing
events, and the Planet 9…
>> QCD axion cosmology! No ne-tuning. (assuming theduring-in ationary scenario)

fifl

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If time allows…

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free particles
collapse of walls bounded by strings
Gravitational Waves

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Gravitational waves are mainly generated during thescaling regime of the string wall-network
scaling regime: roughly one piece of wall per horizon volume

𝒪

A is anShuailiang Ge (PKU)(1) number25

De ne the GW spectrum as,see eg (T. Hiramatsu et al 1207.3166);

At the peak frequency,(Ligong Bian, SG, Changhong Li, Jing Shu, Junchao Zong
2212.07871)

Simulation result of thecorresponding GW spectra(T. Hiramatsu et al 1207.3166)fi

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In the cases below, there is no scaling-regime dynamics.
The network collapse at Ten becomes the dominant source.

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The dynamics of collapse of walls bounded by strings can beparameterized as:

exponential decrease ofthe amplitude due to energy
loss into free particles

oscillationcR ∼ (0.1) inferred from the numerical result of (S. Chang, C. Hagmann,and P. Sikivie hep-ph/9807374)

Lorentz factor of the resultant free axions γa ≈ 3.2, (see e.g., T. Hiramatsu et al, 2012;
M. Kawasaki et al, 2015),

𝒪

Approximately,Shuailiang Ge (PKU)28

GW spectra(SG, 2307.08185)

PTA observations

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GW spectra(SG, 2307.08185)

Sensitivities ofGW interferometry
experiments

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Summary{

Closed walls

String-wallnetwork

PBHs (QCD axion)

Important and Interesting!

Open wallsbounded bystrings

Dark matter (QCD axion)
Stochastic GW (axion-like)backgroundDi erent from that of
the scaling regime

ff

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Backup Slides

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Abundance
open wallsbounded by strings

free axions that
explain dark matter(Keisuke Harigaya, Lian-Tao Wang, 2022),(SG, Jinhui Guo, Jia Liu, 2023)

Lorentz factor γa ≈ 3.2,

(see e.g., T. Hiramatsu et al, 2012; M. Kawasaki et al, 2015),

closed walls

PBHs(SG, Jinhui Guo, Jia Liu, 2023)

If Ωa = ΩDM, we have fPBH = γ ⋅ γa = 2.56 % ,independent of axion parameters and Ten !
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Overproduction of free particles

free particles (“cold”)
collapse of walls bounded by strings
Gravitational Waves

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Overproduction of free particles
To avoid the overproduction, we require free particles to further decay into
relativistic species. (not disturbing BBN)
1. Decay into SM particles:

2. Decay into dark photons:

The resultant dark photons may help alleviate the Hubbletension, see (Ligong Bian, SG, Changhong Li, Jing Shu, Junchao Zong, 2212.07871)
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Future directions
1. A detailed solution of the cosmic evolution of the multiple components (axions
decaying into dark photons) during the BBN epoch. Related to Hubble tension
and dark matter abundance.
2. The GW spectra of gauge strings (i.e., cosmic strings) will also be signi cantly
altered by the scenario of re-entering horizon.
….

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Shuailiang Ge (PKU)