Primordial Black Holes
from 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)
Primordial black holes (PBHs)

inflaton
ρb
\rho_b
ρi
\rho_i
ρb<ρi
\rho_b< \rho_i
radiation
shock
ρ/ρFRW
\rho/\rho_\text{FRW}
r
r
early stage of evolution of ρ
Hb−1
H_b^{-1}
Hb−1
H_b^{-1}
BH
subcritical
Hb−1
H_b^{-1}

subcritical spacetime
shock
Hb−1
H_b^{-1}
supercritical

supercritical spacetime

shock
κRi3, M<M∗
\kappa R_i^3,\ \ \ M< M_*
HiRi2, M>M∗
H_iR_i^2,\ \ \ M> M_*
GM∼
GM\sim
{
\{
BH mass
where
M∗∼GκHi3
M_*\sim \frac{H_i^3}{G\kappa}
lower cutoff
Mmin
M_\text{min}
BH mass distribution
PBH mass function (fraction of CDM in PBH with mass ~ M )
f(M)≡ρCDMM2dMdn∝
f(M)\equiv \frac{M^2}{\rho_\text{CDM}} \frac{dn}{dM}\propto
M∗−1/2, M<M∗
M_*^{-1/2},\ \ \ M< M_*
M−1/2, M>M∗
M^{-1/2},\ \ \ M> M_*
{
\{

PBH constraints

LIGO BH
f(M∼30 M⊙)∼10−3 → merger rate for LIGO events
1603.08338 by Sasaki et al. (2016)
M∗∼M⊙
M_* \sim M_\odot
→ f(M∼30 M⊙)∼10−3
\to \ f(M\sim30\ M_\odot) \sim 10^{-3}
SMBH
M∗<Mseed∼103M⊙,
M_* < M_{\text{seed}} \sim 10^3 M_\odot,
Γ≳10−17
\Gamma \gtrsim 10^{-17}
→ nM∼10−1Mpc−3
\to \ n_M \sim 10^{-1} \text{Mpc}^{-3}
μ distortion
spiky distribution
μmax∼106Γ4/3
\mu_\text{max} \sim 10^6 \Gamma^{4/3}
Primordial Black Holes from 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)
PBHs from Bubbles
By Heling Deng
PBHs from Bubbles
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