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}