KEK / Sokendai / KavliIPMU · 2020. 10. 13. · KEK / Sokendai / KavliIPMU Kazunori Kohri ... KK and T.Terada, 2018 Pulsartiming for 2ndGW µ-distortion of CMB T=T R. The NANOGrav12.5-year

Primordial Black Hole Dark Matter

KEK / Sokendai / Kavli IPMU

Kazunori Kohri(郡 和範)

Why PBHs?

LIGO and Virgo have detected gravitationalwave signals from 30 M◉Binary Black Holes

https://www.youtube.com/watch?v=1agm33iEAuo

GW150914 and its merger rates for 30 Msolar masses BBH

M. Sasaki, T. Suyama, T. Tanaka and S. Yokoyama (2016).A 3-body effect is important for the BBH formations

fraction to CDM (ffraction)

Rate

of

GW15

0914

10-1010-910-810-710-610-510-410-30.01

0.1

1

10

1015 1020 1025 1030 1035 1040 1045 1050 1055

10-15 10-10 10-5 1 105 1010 1015 1020

SN

HSC

K

E

M

O

IRS

S1 Eri

WBGC

G

DH

DF

CMB

IL

XB

PA

GWLy

LSS

GW2

n/p

GGBEGB

V

CMB

f(M)

M [g]

M/M

Upper bounds on the fraction to CDMf P

BH=Ω

PBH/Ω

CDM

MPBH

Carr, Kohri, Sendouda, J.Yokoyama (2020)

30M⊙

GWs

10−5M⊙

OGLE

104.5M⊙

Seed ofSMBH

Gam

ma-

ray/

CMB

GravitationalLensing Accretion Disk

and CMB

LIGO

2nd GW

Acoustc rehearing CMB µ- distortion

Mass in gram

1017gDM

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

Primordial Black Hole (PBH)• Large perturbation at small scales

was produced by Inflation at around > 10-36 second

2020/10/13 Kazunori Kohri (KEK/Sokendai)

Conditions for a PBH formation in Radiationdominated (RD) Universe

• Gravity could be stronger than pressure

Horizon size = H-1 = (k/a)-1

A fluctuation with the wave number k

δ > δc ~ p / ρ ~ cs2 = w = 1 / 3

Black Hole

A closed universe immediatelycollapsing into a BH

Harada,Yoo and KK (2013)

Zel’dovich and Novikov (1967), Hawking (1971), Carr (1975)

δ

Typical quantities of PBHs in RD• Mass (horizon mass =ρ(tform) H(tform)-3 )

• Fraction to CDM

M

PBH~ M

pl2 t

from~

Mpl3

T 2form

~ 1015 gT

form

3× 108GeV

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−2

~ 30M⊙

Tform

40MeV

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−2

ffraction ⌘⌦PBH⌦CDM

⇠ 108✓MPBH30M�

◆�1/2 pP⇣ exp

� 118P⇣

�

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

P⇣ ⇠< ⇣2 >⇠< �2 >⇠< (�T/T )2 >

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

Curvature perturbation Pζ

KK and T.Terada, 2018

Am

plit

ude

of c

urva

ture

pert

urba

tion

wave number k = p x a

Planck (2015)

at 68% C.L.

For inflation modelswith a big running,see Kohri, Lin Lyth(2008)

P⇣ ⇠< ⇣2 >⇠< �2 >⇠< (�T/T )2 >

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

100 % Dark Matter by PBHs with1017 g masses

KK and T.Terada, 2018

Pulsar timingfor 2nd GW

µ-distortionof CMB

T=TR

The NANOGrav 12.5-year Data Set:Search For An Isotropic Stochastic Gravitational-Wave Background

2020/10/13 Kaz Kohri (KEK)

Zaven Arzoumanian, et al, The NANOGrav Collaboration, arXiv:2009.04496

γ = 3 – 2α = 5 – β

Secondary gravitational wave (GW) nonlinearly-induced by large

curvature perturbation Pζ• Energy density of GWs

Relevant when Pζ >> tensor to scalar ratio r

scalar x scalar modes

⌦GW,c(f) =1

12

✓f

2⇡aH

◆2 Z 1

0dt

Z 1

�1ds

"t(t+ 2)

�s2 � 1

�

(t+ s+ 1)(t� s+ 1)

#2

⇥ I2 (t, s, k⌘c)P⇣✓(t+ s+ 1)f

4⇡�

◆P⇣

✓(t� s+ 1)f

4⇡

◆

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

NANOGrav12.5yr and solar mass PBHs

2020/10/13 Kaz Kohri (KEK)

K. Kohri and T. Terada, arXiv:arXiv:2009.11853

MPBH ⇠ O(1)M�✓

k

107Mpc�1

◆�2⇠ O(1)M�

✓5⇥ 10�9Hz

f

◆2

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

- - - - -×-

× -× -

× -× -

× -× -

PBH+

GW

ffraction ⌘⌦PBH⌦CDM

⇠ 108✓MPBH30M�

◆�1/2 pP⇣ exp

� 118P⇣

�

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

⌦GW,c(f) =1

12

✓f

2⇡aH

◆2 Z 1

0dt

Z 1

�1ds

"t(t+ 2)

�s2 � 1

�

(t+ s+ 1)(t� s+ 1)

#2

⇥ I2 (t, s, k⌘c)P⇣✓(t+ s+ 1)f

4⇡�

◆P⇣

✓(t� s+ 1)f

4⇡

◆

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

NANOGrav12.5yr and solar mass PBHs

2020/10/13 Kaz Kohri (KEK)

K. Kohri and T. Terada, arXiv:arXiv:2009.11853

MPBH ⇠ O(1)M�✓

k

107Mpc�1

◆�2⇠ O(1)M�

✓5⇥ 10�9Hz

f

◆2

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

2020/10/13 Kaz Kohri (KEK)

NANOGrav12.5yr and solar mass PBHsK. Kohri and T. Terada, arXiv:arXiv:2009.11853

Merger GWs

secondary GWs

fPBH=

Summary

• PBH can be produced by large curvature perturbation ζ ~O(1) at small scales in the early Universe

• PBHs with mPBH >O(10) M◉ : LIGO/Virgo

• PBHs with mPBH ~O(1017)g - O(1020)g : DM

• PBHs with mPBH ~O(10-5) M◉ : OGLE events

• PBHs with mPBH ~O(104) M◉ : seeds of SMBH

• PBHs with mPBH ~O(1) M◉: NANOGrav12.5

Typical quantities of PBHs in RD• Mass (horizon mass =ρ(tform) H(tform)-3 )

• Lifetime

• Hawking Temperature

• Fraction to CDM

M

PBH~ M

pl2 t

from~

Mpl3

T 2form

~ 1015 gT

form

3× 108GeV

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−2

~ 30M⊙

Tform

40MeV

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−2

T

PBH~

Mpl2

MPBH

~ 0.1MeVM

PBH

1015 g

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−1

~ 3× 10−11KM

PBH

30M⊙

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−1

τ

PBH~

M3PBH

Mpl4

~ 4 × 1017 secM

PBH

1015 g

⎛

⎝⎜⎜

⎞

⎠⎟⎟

3

~ 3× 1068yrsM

PBH

30M⊙

⎛

⎝⎜⎜

⎞

⎠⎟⎟

3

f

fraction≡Ω

PBH

ΩCDM

~ β10−18

⎛

⎝⎜

⎞

⎠⎟

MPBH

1015 g

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−1/2

~ β10−8

⎛

⎝⎜

⎞

⎠⎟

MPBH

30M⊙

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−1/2

~ 108M

PBH

30M⊙

⎛

⎝⎜⎜

⎞

⎠⎟⎟

−1/2

Pδ

exp − 118P

δ

⎡

⎣⎢⎢

⎤

⎦⎥⎥