Primordial Black Hole Formation by Vacuum Bubbles

Heling Deng

1804.10059  with Alex Vilenkin and Masaki Yamada (2018)

Tufts University

1710.02865  with Alex Vilenkin (2017)

1612.03753  with Jaume Garriga and Alex Vilenkin (2016)

1512.01819  by Jaume Garriga, Alex Vilenkin and Jun Zhang (2016)

inflaton

\rho_b
\rho_i
\rho_b< \rho_i

radiation

shock

\rho/\rho_\text{FRW}
r

early stage of evolution of \(\rho \)

H_b^{-1}
H_b^{-1}

BH

subcritical

H_b^{-1}

subcritical spacetime

shock

H_b^{-1}

supercritical

supercritical spacetime

shock

\kappa R_i^3,\ \ \ M< M_*
H_iR_i^2,\ \ \ M> M_*
GM\sim
\{

BH mass

where

M_*\sim \frac{H_i^3}{G\kappa}

lower cutoff

M_\text{min}

BH mass distribution

PBH mass function (fraction of CDM in PBH with mass ~ \(M\) )

f(M)\equiv \frac{M^2}{\rho_\text{CDM}} \frac{dn}{dM}\propto
M_*^{-1/2},\ \ \ M< M_*
M^{-1/2},\ \ \ M> M_*
\{

PBH constraints 

LIGO BH

\(f(M\sim 30\ M_\odot) \sim 10^{-3} \ \to \)  merger rate for LIGO events

1603.08338 by Sasaki et al. (2016)

M_* \sim M_\odot
\to \ f(M\sim30\ M_\odot) \sim 10^{-3}

SMBH

M_* < M_{\text{seed}} \sim 10^3 M_\odot,
\Gamma \gtrsim 10^{-17}
\to \ n_M \sim 10^{-1} \text{Mpc}^{-3}

\( \mu \) distortion

spiky distribution

\mu_\text{max} \sim 10^6 \Gamma^{4/3}
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