PBHs from Primordial Bubbles

Primordial Black Holes from Primordial Bubbles

Heling Deng

Arizona State University

Primordial black holes

PBHs from bubbles

Gravitational waves from PBHs

Conclusions

Primordial black holes

PBHs from bubbles

Gravitational waves from PBHs

Conclusions

Black Hole

A region of spacetime from which no particles can escape due to strong gravity

-- Prediction of the theory of general relativity

Can be formed by dying stars: astrophysical BHs with mass

\sim 10 \ M_\odot

Supermassive BHs were discovered at galactic centers with mass

\sim 10^6\text{-}10^{11} \ M_\odot

which cannot be explained by astrophysical BHs

wikipedia

astro.uchicago.edu

Primordial black holes

PBHs from bubbles

Gravitational waves from PBHs

Conclusions

Physics beyond the "standard model" at high energy

Phase transition in the early universe \(\to\) Bubbles

quantum tunneling

Fate of the bubble

subcritical

supercritical

Fate of the bubble

subcritical

supercritical

\(\Delta s^2\)= \(A^2(t,r)\Delta t^2 - B^2(t,r)\Delta r^2 - R^2(t,r)(\Delta \theta^2 + \sin\theta\Delta \phi^2)\)

Spherical spacetime (\(t,r,\theta,\phi\))

Radiation fluid: \(p=\frac{1}{3}\rho\)

\frac{A'}{A}=-\frac{\rho'}{4\rho}

\dot{U}=-A\left(\frac{4}{3}\pi\rho R+\frac{M}{R^2} \right)+\frac{A'\Gamma}{B}

\dot{\Gamma}=\frac{A'U}{B}

\dot{R}=AU

\dot{B}=\frac{AU'}{\Gamma}

\dot{\rho}=-\frac{4}{3}\rho A\left(\frac{U'}{B\Gamma}+\frac{2U}{R} \right)

where

U\equiv \frac{\dot{R}}{A}

\Gamma \equiv \frac{R'}{B}

M\equiv \frac{R}{2}\left(1-\Gamma^2 + U^2\right)

\rho/\rho_\text{FRW}

Early stage of evolution of \(\rho \)

\rho/\rho_\text{FRW}

Evolution of \(\rho \) after BH formation (subcritical)

\rho/\rho_\text{FRW}

Evolution of \(\rho \) at late time (subcritical)

m\propto R^3

m\propto R^2

BH mass as a function of model parameters + Size distribution of bubbles\(\to\) BH mass distribution

\(\sim 10M_\odot\)

Primordial black holes

PBHs from bubbles

Gravitational waves from PBHs

Conclusions

LIGO BHs

Mass distribution of LIGO BHs

PBH binary

Dataset

Event: \((m_1,m_2,z)\)

Mass distribution of LIGO BHs

m^{\alpha_1},\ \ \ m< m_*

m^{\alpha_2},\ \ \ m> m_*

f(m)\propto

A simple mass function

\log(m)

\log(f)

m^{\alpha_1}

m^{\alpha_2}

m_*

f_{PBH}

PBH mass function

Merger rate

Detection probability

Probability of each event \(p_i(m_1,m_2,z)\)

Likelihood of all LIGO events

Expected number of detection \(N_e\)

p_{Poisson}\propto N_e^{N_o}e^{-N_e}

\mathcal{L}\propto p_{Poisson}\prod_{i=1}^{N_o} p_i

Mergers reaching earth today

Signals follow a Poisson process

f_{PBH}\approx 10^{-3}

Maximizing \(\mathcal{L}\) in a 4-parameter space

\alpha_2 = -4

\alpha_1 = 1.2

m_*=35M_\odot

\log(m)

\log(f)

m^{1.2}

m^{-4}

35M_\odot

10^{-3}

Is there a mechanism that can provide such a mass function?

subcritical

supercritical

Conclusions

Primordial bubbles can be formed in the early universe due to phase transition

Depending on their sizes after the big bang, bubbles can be classified into two categories: subcritical and supercritical, both leading to black hole formation

PBH mass spectrum can range over many orders of magnitude

With some parameter choices, these PBHs can account for SMBHs and black hole mergers observed by LIGO