2023.12.05 @ Kashiw Dar Mae Symposiu 2023

The Present & Future of

Primordial Black Holes as Dark Matter

Nagoya U. IAR

Yuichiro TADA

Escrivà, Kühnel , YT “Primordial Black Holes” (2022)"Black Holes in the Era of Gravitational-Wave Astronomy"

Contents
1.

Self-Introduction

2. PBH as DM
3. PBH and Inflation
4. Recent Topics
5. Summary

Yuichiro TADA 多田 祐一郎’08-’12

Undergrad @ UTokyo’12-’17

PhD w/ H. Murayama (IPMU), M. Kawasaki (ICRR)’17-’18

PD w/ S. Renaux-Petel (IAP)’18-’21

JSPS PD w/ N. Sugiyama (Nagoya)‘21-

YLC Assistant Prof. w/ K. Ichiki (Nagoya)on Early Universe Inflation, PBH, GW, …
PBH as DM — Yuichiro TADA

1. Self-Introduction

3 /37

2. PBH as DM

Primordial BH
Carr & Hawking ’74

PBH as DM — Yuichiro TADA…

…

- ∼ 𝒪(1) Primordial PTBs (Carr ‘75)
- Dark Matter (Chapline ‘75)
- Isocurvature (Dolgov & Silk ‘93)
- LVK merger GW? (Sasaki+ ’16)
- Quark Confinement (Dvali+ ’21)
- SMBH seeds? (Düchting ‘04)
- Collapse of topological defect (Hawking ‘89)
- OGLE lensing obj.? (Niikura+ ‘19)
- Bubble collision (Hawking+ ‘82)
- Planet 9? (Scholtz & Unwin ‘19)
- Particle trapping in bubble (Baker+ ‘21)
- Trigger of r-process? (Fuller+ ‘17)
- Asynchronous 1st PT (Liu+ ‘21)
- Baryogenesis? (Baumann+ ‘07)
- Scalar 5th force (Flores & Kusenko ’20)
before Star Form.
- JWST luminous gals? (Hutsi+ ‘22)
Primordial Black Hole
2. PBH as DM

5 /37

Primordial BH
Carr & Hawking ’74

338 in 2023

PBH as DM — Yuichiro TADA…

…

- ∼ 𝒪(1) Primordial PTBs (Carr ‘75)
- Dark Matter (Chapline ‘75)
- Isocurvature (Dolgov & Silk ‘93)
- LVK merger GW? (Sasaki+ ’16)
- Quark Confinement (Dvali+ ’21)
- SMBH seeds? (Düchting ‘04)
- Collapse of topological defect (Hawking ‘89)
- OGLE lensing obj.? (Niikura+ ‘19)
- Bubble collision (Hawking+ ‘82)
- Planet 9? (Scholtz & Unwin ‘19)
- Particle trapping in bubble (Baker+ ‘21)
- Trigger of r-process? (Fuller+ ‘17)
- Asynchronous 1st PT (Liu+ ‘21)
- Baryogenesis? (Baumann+ ‘07)
- Scalar 5th force (Flores & Kusenko ’20)
before Star Form.
- JWST luminous gals? (Hutsi+ ‘22)
Primordial Black Hole
2. PBH as DM

6 /37

Obs. Consts.

Rep. Prog. Phys. 84 (2021) 116902

Review

PBH / All DM

All DM = PBH

Carr, Kohri, Sendouda, Yokoyama ‘20
Constraints
on f (M) from evaporation (red), lensing (magenta), 2.
dynamical
PBH asFigure
DM —10.Yuichiro
TADA
PBH aseffects
DM (green), gravitational waves (black), accretion
7 /37

Positivist Perspective?

EW
100
Observational Evidence for Primordial Black Holes

80

QCD

g*
g*s

60
40

e +e − anni.

20
0

0.32
0.30

Carr, Clesse, García-Bellido, Hawkins, Kühnel ‘23

Figure 38. PBH mass function with peaks induced by the thermal history of the Universe (thick, dashed curve;
cf. Ref. [34]). Figure includes the same pieces of positive evidence for PBHs as in Fig. 1. Also included, as acomparison, are various monochromatic constraints on fPBH (M ) (light-shaded regions), taken from Ref. [371].
D.

0.28

Comparing Evidence with Thermal-History Model

In Figs. 1 and 38, we have indicated the PBH mass and dark matter fraction required to explain thevarious type of observational evidence discussed in this review. We now explain the derivation of theseregions in more detail, considering the lensing, dynamical and GW arguments in turn. However, just
as for PBH constraints, all these estimates are based on various assumptions and subject to significant
uncertainties. In particular PBH properties (such as mass function, clustering etc.) can modify thedi↵erent regions. Unless indicated otherwise, we assume a monochromatic PBH mass function.
PBH dark matter fraction from lensing evidence. We have estimated the PBH dark matter
fraction for six types of lensing evidence in the following way:
• For HSC, we have reinterpreted the limits of Ref. [96]. Instead of assuming no detection, we havecomputed the 2 confidence intervals for fPBH assuming that one PBH microlensing event wasobserved. The limit is identified with a band using simple Poisson statistics. All the assumptions
are therefore identical to those of Ref. [96].

0.26
0.24
10-6

w
c2s
0.001

1
T [GeV]cf. Saikawa & Shirai ‘18• For OGLE, we show the 2 allowed region provided in Fig. 8 of Ref. [93], combining the OGLE
confidence region with the HSC exclusion region

PBH as DM — Yuichiro TADA

– 75/107 –2. PBH as DM

1000

8 /37

Evidence? 1

3

M < M⊙TABLE I. The candidates of the search with a SNR > 8 and a FAR < 2 yr 1 . We report here the FAR, ln L, the UCT time ofthe event (date and hours), template parameters that pick the events and the associated SNRs.
FAR [yr

1

]

ln L

0.16748.457
0.21938.2
L20 0.4134
LVK 7.585
1.2148
6.589

UTC time

mass 1 [M ] mass 2 [M ]2017-03-15 15:51:30
2017-07-10 17:52:43
2017-04-01 01:43:34
2017-03-08 07:07:18

3.062
2.106
4.897
2.257

0.92810.27590.77950.6997

spin1zspin2z0.08254 -0.09841
0.08703 0.0753-0.05488 -0.04856-0.03655 -0.04473

Network SNR H1 SNR L1 SNR
8.527
8.157
8.672
8.535

8.527
6.319
6.321

8.157
5.939
5.736

Table 1. The triggers with a FAR < 2 yr 1 in at least one search pipeline. We include the search-measured parameters associatedwith
Phukon+ ‘21
each candidate: m1 and m2 , the redshifted component masses, and 1 andcomponent spin. The parameters shown+0.46 2 , the dimensionless+0.12(Prunier+’23)denote the Hanford,
m2 the= 0.27M⊙H,
1 = 0.62
in the table are the ones reported by the search where themtrigger
is identified
lowest
FAR.
L, and V−0.20 M⊙,with−0.10
Livingston, and Virgo interferometers, respectively. The dashes in the “V SNR”
mean thanthat NSno single-detector trigger was found ineven lighter
m2 iscolumn
Advanced Virgo. The network SNR is computed by adding the SNR of single detector triggers in quadrature.
FAR [yr
0.20
1.37
1.56

1]

Pipeline

GPS time

m1 [M ]

m2 [M ]

1

2

H SNR

L SNR

V SNR

Network SNR

GstLALMBTA
GstLAL

1267725971.02
1259157749.53
1264750045.02

0.78
0.40
1.52

0.23
0.24
0.37

0.57
0.10
0.49

0.02
0.05
0.10

6.31
6.57
6.74

6.28
5.31
6.10

5.81
-

8.90
10.25
9.10

LVK ‘22

3 SENSITIVITY AND RATE LIMITS

as DM of— significant
Yuichiro TADAThePBHabsencecandidates in O3b allows us to2. PBH as DM

9 /37

Evidence? 2Merger rate [Gpc

-3

-1

yr ]

Redshift dependence
100
50Stellar (upper limit)
Stellar (lower limit)

10
5

Stellar
PBH binaries (high z) fPBH =10-3
PBH binaries (low z) fPBH =1, model A

1
0.5
0

PBH binaries (low z) fPBH =1, model B

1

2

3
z

4

5

6
Sasaki, Suyama, Tanaka, Yokoyama ‘18

Figure20:
dependence of the merger rate2.ofPBHthe
BH-BH binaries per unit source
PBH asDM Redshift— Yuichiro TADA
as DM
10 /37 time(indirect) Evidence? 3

δρ
∼1
ρ

20

if MBH ∼ 10 g
→ 100% Dark Matter

induced GW b.g.

LISA

PBH as DM — Yuichiro TADA

−2

𝒫ζ ∼ 10

Radiation Era

2. PBH as DM

11 /37

3. PBH & Inflation

Co

sm

Or ic
igi Infl
no a
f fl tio
uc n
tu
at
ion

s

What’s Inflation?

• Accelerated Expansion of the Early U.
• Did it really happen?
• What kind of obj. drove it?

PBH as DM — Yuichiro TADA

3. PBH and Inflation

13 /37

Generation of PTB“Horizon” of the expanding U.
PBH as DM — Yuichiro TADA

3. PBH and Inflation

14 /37

Generation of PTB“Horizon” of the expanding U.
PBH as DM — Yuichiro TADA

3. PBH and Inflation

15 /37

Generation of PTB

micro Quantum perturbation“Horizon” of the expanding U.
PBH as DM — Yuichiro TADA

3. PBH and Inflation

16 /37

Generation of PTB

Macro “Classical” perturbationcf. Schrödinger’s Cat“Horizon” of the expanding U.
PBH as DM — Yuichiro TADA

3. PBH and Inflation

17 /37

Generation of PTB？

“Horizon” of the expanding U.
PBH as DM — Yuichiro TADA

3. PBH and Inflation

18 /37

Generation of PTB
Gravity

Energy = Mass
H size during inflation

current H size
PBH as DM — Yuichiro TADA

3. PBH and Inflation

20 /37

Large PTB?
Lyth, Malik, Sasaki ‘05

V- Time shift δN(x) is conserved on superH- Equivalent to Curv. PTB ζ(x)

δϕ(x)

·a
e-folds: dN = Hdt = dta2
222ζ(t,x) 2
local U.: ds = − dt + a (t)edx

end of infl.

SM

PBH as DM — Yuichiro TADA

ϕ

δϕ(x)
ζ(x) = δN(x) ≃ − H ·ϕ
3. PBH and Inflation

21 /37

Exp.-tail·ϕ is reducing → δϕ’s effect is asymmetric!
0.01

CMB
P(ζ)

V

∝ exp (−Λζ) : exp-tail

10-7
10-12
-17

10

ζ2
∝ exp − 2 : Gaussian( 2σ )

10-22

PBH
ϕ
PBH as DM — Yuichiro TADA

- 0.5

0.0

0.5

ζ

1.0

1.5

cf. Pattison+ ’17, Atal+ ‘19

δϕ → ζ = δN : non-linear relation
3. PBH and Inflation

23 /37

Triangle study
V

Universal Criterion

Atal+ ’19
Escrivà, YT, Yokoyama, Yoo ‘22

inflation model2
𝒞(r) = [1 − (1 + rζ′(r))2]
3
Rm
1
2
2
¯
¯
𝒞=
4πR 𝒞dR > 𝒞th =VRm ∫05

ϕ

Non-PTB??

Mass Formula Choptuik+ ‘93

Abe, Inui, YT, Yokoyama, Yoo ‘22¯ −𝒞¯ th)0.36
M ∼ MRm(𝒞

10-8

Num. Rel.
ΩGW h2

10-10

The total of the exponential tail
Pure Gaussian! "! "

10-12! "! #
LISA! "! $

PTB □ ĥ = Sζ̂
PBH abundance
PBH as DM — Yuichiro TADA

10-14
DECIGO

10-16 -4
1. × 10

5. × 10-4

0.001

0.005

f [Hz]

indirect evidence
3. PBH and Inflationinduced GW b.g.
24 /37

Stochastic Approach = EFT of superH fields
Starobinsky ’86= Local FRLW + Correlated Brownian motiondϕ(N, x)dπ(N, x)2 2
3MPlH (N, x)dW(N, x)dW(N′, y)

PBH as DM — Yuichiro TADA

π(N, x)=dN +H(N, x)H(N, x)≈2π𝒫ϕ(N, x)dW(N, x),V′(ϕ(N, x))= −3π(N, x) −dN,(
H(N, x) )1 2= π (N, x) + V(ϕ(N, x)),2
sin kσ(N) | x − y |=δNN′dNkσ(N) | x − y |3. PBH and Inflation

25 /37

STOLAS
Mizuguchi, Murata, YT in prep.

1 2 2
Ex. 1: Chaotic V = m ϕ2ζ0.0004
2. × 10-8

P R E L I M I N A R Yζ

0.0002

1. × 10-8

0

P
E
L
I
M
I
N
A
R
Y
-9 R
5. × 10-0.0002

2. × 10-91-0.0004

PBH as DM — Yuichiro TADA

3. PBH and Inflation

2

5
n

10

20

26 /37

STOLAS
Mizuguchi, Murata, YT in prep.

V

Ex. 2: Starobinsky’s linear

Starobinsky ‘92

ϕ

ζ
0.50

0.020

0.25

0.010

ζ

P R E L I M I N A R Y

0.050

0

0.005 P

-0.25

0.002

-0.50

PBH as DM — Yuichiro TADA

R E L I M I N A R Y

1

3. PBH and Inflation

2

5
n

10

20

27 /37

Ex. 1 : Chaotic

Ex. 2 : Starobinsky’s linearζζ

0.00040.50

P R E L I M I N A R Y

0.0002P R E L I M I N A R Y 0.25

0

0

-0.25

-0.0002-0.50-0.0004

PBH as DM — Yuichiro TADA

3. PBH and Inflation

28 /37

Importance Samplingsee, e.g., Jackson+ ‘22

Ex. 2 : Starobinsky’s linear

Intentionally large noise @ N = 42¯ m = 0.56 > 𝒞¯ th =
ζ(r) → 𝒞(r) → 𝒞
5P R E L I M I N A R Y
Probability is re-weighted
according to the probability of large noise!!

PBH as DM — Yuichiro TADA

3. PBH and Inflation

29 /37

Triangle study
V

Universal Criterion

Atal+ ’19
Escrivà, YT, Yokoyama, Yoo ‘22

inflation model2
𝒞(r) = [1 − (1 + rζ′(r))2]
3
Rm
1
2
2
¯
¯
𝒞=
4πR 𝒞dR > 𝒞th =VRm ∫05ϕ

STOLAS + importance sampling

Mass Formula Choptuik+ ‘93¯ −𝒞¯ th)0.36
M ∼ MRm(𝒞Abe, Inui, YT, Yokoyama, Yoo ‘22

P R E L I M I N A R Y

10-8

Num. Rel.
ΩGW h2

10-10

The total of the exponential tail
Pure Gaussian! "! "

10-12! "! #
LISA! "! $

PTB □ ĥ = Sζ̂
PBH abundance
PBH as DM — Yuichiro TADA

10-14
DECIGO

10-16 -4
1. × 10

5. × 10-4

0.001

0.005

f [Hz]

indirect evidence
3. PBH and Inflationinduced GW b.g.
30 /37

4. Recent Topics

Draft version June 29, 2023
Typeset using LATEX twocolumn style in AASTeX63
Draft version June 29, 2023
Typeset using LATEX twocolumn style in AASTeX63

Tensorial PTB

2306.16213

The NANOGrav
for a Gravitational-Wave
Background
4 15-year Data Set: Evidence
The NANOGrav
Collaboration

13.8

14 14 14 14 14 13.8 .6 .4 .2 .0 .8

log10 AGWB

3cf. European,
Parkes (Australia),
Gabriella Agazie,1 Akash Anumarlapudi,1 Anne M. Archibald,2 Zaven
Arzoumanian,
PaulChinese
T. Baker,4
6
7, 8 Set: Evidence 9for a Gravitational-Wave
10, 11
5The Blecha,
NANOGrav
15-year
Data
Background
Bence Bécsy,5 Laura
Adam
Brazier,Paul
R.
Brook,
Sarah
Burke-Spolaor,
Rand
Burnette,
(b)
(a)
(c)
5
12
7
13
10, 11Robin Case, Maria Charisi,
Shami Chatterjee,1 Katerina Chatziioannou,
Belinda D. 3Cheeseboro,
1
2
Gabriella14Agazie, Akash Anumarlapudi,
Anne 7M. Archibald, Zaven
Arzoumanian, Paul T.17Baker,415
16
Siyuan Chen,5 Tyler Cohen,6 James M. Cordes,
Neil J. Cornish,
Fronefield Crawford,
7, 8
910, 11
5
𝛾
=
13/3
GWB
Bence Bécsy, Laura
Blecha,Adam
Brazier,Paul
R.
Brook,
Sarah
Burke-Spolaor,
Rand
Burnette,
7, ⇤18
19, 1320
5
H. Thankful Cromartie,
Kathryn12Crowter, Curt J.
Megan E. DeCesar,
Dallas DeGan,
7 Cutler,
13
10, 11Robin Case,5 Maria
Charisi,
Shami
Chatterjee,
Katerina
Chatziioannou,
BelindaD.
Cheeseboro,
21
522, 2324, 2526
Paul B. Demorest,
HelingDeng,
Timothy
Dolch,
BrendanDrachler,
JustinA.
Ellis,
157
16
17
Siyuan Chen,1427,Tyler
Cohen,
James
M.
Cordes,Neil
J.
Cornish,Fronefield
Crawford,
28, 2910, 11
10, 11
1
7, ⇤ William Fiore,
18 Emmanuel Fonseca,
19, 1320
5ElizabethC.
Ferrara,GabrielE.
Freedman,
H. Thankful10,Cromartie,
Kathryn
Crowter,
Curt
J.
Cutler,Megan
E.
DeCesar,Dallas
DeGan,
11
10, 115
12
10,24,
1125
30, 31
21
22, 2326
Nate Garver-Daniels,
Peter
A.
Gentile,Kyle
A.
Gersbach,
JosephGlaser,DeborahC.
Good,Paul B. Demorest, Heling Deng, Timothy Dolch,
Brendan Drachler,
Justin A. Ellis,
32
5
13
1
10, 11,1†
27, 28, 29
10, 11
10, 11Kayhan Gültekin,JeffreyS.
Hazboun,SophieHourihane,
Kristina
Islo,
Ross
J.
Jennings,
Elizabeth C. Ferrara,
William Fiore,
Emmanuel Fonseca,
Gabriel E. Freedman,
1, 13
10, 11
10, 11 L. Jones,1 Andrew
10, 11
12L. Kaplan,1 Luke
10, 11Zoltan Kelley,33 30, 31
AaronNateD. Johnson,
Megan
R.
Kaiser,David
Garver-Daniels,
Peter A. Gentile,
Kyle A. Gersbach, Josephf Glaser,
Deborah C. Good,
1
=
1
yr
32
nHz
≈
ref
34
35
5
24, 125
12 †
32
51
13
10, 11,
Matthew Kayhan
Kerr, GJoey
S.
Key,
Tonia
C.
Klein,
Nima
Laal,
MichaelT.
Lam,WilliamG.
Lamb,ültekin, Jeffrey S. Hazboun, Sophie Hourihane, KristinafrefIslo,J. Jennings,
1= 0.1 yr Ross
3.2 nHz
≈
19
361
1, 13
1 11
D. Johnson,
Megan L. Jones,
AndrewB.R.Littenberg,
Kaiser,10, 11 37
David
L. Kaplan,
Luke
ZoltanKelley,3833
T. Joseph Aaron
W. Lazio,
Natalia
Lewandowska,
Tyson
Tingting
Liu,10,AndreaLommen,
34
35
1
5
24,
12
10,Joey
11
39,Tonia‡
40
33, T.
41 Lam,2.5
3.025 William
3.5
4.0 G. 42
4.5
Matthew
Kerr,
S.
Key,
C.
Klein,
Nima
Laal,
MichaelLamb,
Duncan R. Lorimer,
Jing Luo,
Ryan S. Lynch, Chung-Pei Ma,
Dustin R. Madison,
19
36 1
10, 1138
gGWB
10, Natalia
11
43,3744Tingting Liu,
10,
11
T.
JosephW.
Lazio,
Lewandowska,
Tyson
B.
Littenberg,
AndreaLommen,Margaret A. Mattson,
Alexander McEwen, James W. McKee,
Maura A. McLaughlin,
39,45
‡
40
33, 4142
12 Lorimer,10, 11 Jing Luo,18,
13
31, 30, 46
DuncanR.
Ryan
S.
Lynch,
Chung-Pei
Ma,
DustinR.
Madison,Natasha McMann, Bradley W.
Meyers,Patrick 1M. Meyers,M.
F. mainMingarelli,Figure Chiara
1. Summaryof theBayesianand optimal-statistic
analyses
(b)
(d)
10,
11
43,
44
10,
11
47
48,
49
50W.
51
7
Margaret
A.
Mattson,Alexander
McEwen,James
McKee,MauraA.
McLaughlin,ofevidenceforthepresenceofHellings–Downs
correlationsin the 15-ye
AndreaMitridate,Priyamvada
Natarajan,
Cherry
Ng,
David
J.
Nice,
StellaKoch
Ocker,
Supermassive
BH
binary12
18, 4513
31, 30, 46−1 Natasha
52
53
54
12
12 1/2/3 regions, ev
McMann,BradleyW.
Meyers,Patrick
M.
Meyers,
ChiaraM.
F.
Mingarelli,
68.3%,
95.4%,
and99.7%
regionsof
distributions
as
GW b.g. Timothy 47T. Pennucci, Benetge 48,∼ nHz (Ken
∼ yrD. )Olum,
B.49P. Perera,
Polina Petrov,
Nihan S. Pol,
50
51
7
𝛾
=
13/3
GWB Ng,analysis,
showingviolins)of independent
Andrea Mitridate,Priyamvada56Natarajan,
CherryDavid
J.posteriors
Nice, (grayStellaKoch
Ocker,
55
34
57
1 variance parame
Henri A. Radovan, Scott
M. Ransom, Paul
Joseph atD.frequencies
Romano,Shashwat
Sardesai,
52
53 S. Ray,
54
12 C.
12 The blue repre
i/T
,
with
T
the
total
data
set
time
span.
Ken D. Olum,
TimothyT.
Pennucci,
Benetge
B.
P.
Perera,PolinaPetrov,
Nihan
S.
Pol,
58
59
12
10, 11, 60
Ann Schmiedekamp,58 Carl Schmiedekamp,
Kai
Schmitz,
Levi
Schult,Brent
J.
Shapiro-Albert,
55
56
34
57the dashed black line corresponds
1 to aforapower-lawmodel;
= 13/
Henri
A.
Radovan,Scott
M.
Ransom,
Paul
S.
Ray,
JosephD.
Romano,ShashwatC.
Sardesai,
1
61, §
62
18
63
PBHXavieras DM —Siemens,
Yuichiro5,TADA
4.
RecentTopics32/37
posterior
amplitude.
See
§3
for
more
details.
(b):
Posterior
Joseph58Simon,
Magdalena
IngridH. Stairs,
Daniel R. Stinebring,10,58 S. Siwek,
59
12
11, 60probability dE] 28 Jun 2023

.HE] 28 Jun 2023

Pulsar Timing Array

Typeset using LATEX twocolumn style in AASTeX631

Pulsar Timing Array

2306.16219

The NANOGrav 15-year Data Set: Search for Signals from New Physics
1, 2

3

3

NANOGrav 15-year New-Physics
45

log10 A

h2

GW

h2

GW

Adeela Afzal,
Gabriella
Agazie,Akash
Anumarlapudi,
Anne
M.
Archibald,
Zaven
Arzoumanian,
15-year New-Physics Signals
11
6 NANOGrav
78, 9, 1011
12
induced
GWs
sigw-delta+smbhb
Paul T.6 Baker, Bence Bécsy, Jose Juan Blanco-Pillado,
Laura Blecha, Kimberly
K. Boddy,
10
13, 1415
16, 17
7
sigw-delta 7
dam Brazier,Paul
R.
Brook,
Sarah
Burke-Spolaor,
Rand
Burnette,
Robin
Case,
Maria
Charisi,
lisa
10 8
13
19
16, 1720
21
decigoShami Chatterjee,
Katerina Chatziioannou, Belinda
D. Cheeseboro,
Siyuan Chen, Tyler Cohen,
10
bbo
10
13
22
23
13, ⇤
et
mes M. Cordes,
Neil J. Cornish, Fronefield Crawford, H. Thankful Cromartie,
Kathryn Crowter
1210ce
25, 19
26
7
27
7
Curt
J. Cutler,
Megan E. DeCesar, Dallas
DeGan, Paul B. Demorest, Heling Deng,
hlvk
14
10
28, 2930, 3132
33, 34, 35
hlv(o)
Timothy
Dolch,
BrendanDrachler,
RichardvonEckardstein,
ElizabethC.
Ferrara,16
10
16, 1716, 173
16, 17
WilliamFiore,
Emmanuel
Fonseca,
GabrielE.
Freedman,NateGarver-Daniels,
igw
sigw-delta
pt-bubble
pt-sound10 18616, 1718
16, 1736, 3738
10Peter A. Gentile,
Kyle A.
Gersbach, Joseph Glaser,
Deborah C. Good,
Lydia Guertin,f [Hz]
839
7
19
3
16, 17, †10
Kayhan Gültekin, Jeffrey S. Hazboun, Sophie Hourihane,
Kristina
Islo,
Ross
J.
Jennings,
NG15
017
10
3,
19
3
16,
Aaron10D. Johnson,
Megan L. Jones, Andrew R. Kaiser,David L. Kaplan,3 Luke Zoltan Kelley,40
12
31
18
25
10
Matthew Kerr,41 Joey S. Key,42 Nima Laal,7 Michael T. Lam,30,
WilliamG.
Lamb,T.
JosephW.
Lazio,
1
14
fPBH = 1194344, 3245
10Vincent S. H. Lee, Natalia Lewandowska, Rafael R. Lino dos Santos,
Tyson B. Littenberg,
16, 1716, 1746, ‡247
40, 4810 16
Tingting
Liu,
DuncanR.
Lorimer,
Jing
Luo,
Ryan
S.
Lynch,
Chung-Pei
Ma,
stable-n
super
dw-sm
dw-dr
10 18
49
3
fPBH50,= 151 Maura A. McLaughlin,16, 17
DustinR.
Madison,Alexander
McEwen,James
W.
McKee,
410 10
10 8
10 618 10 4
10 2
1
102
1052
106
24,
19
37, 36, 53
Natasha McMann, Bradley
W. Meyers,
Patrick M. Meyers,
M. F.2 Mingarelli,
98 Chiara
7
6
1
0f [Hz]
5412
55,
56 f⇤ /Hz
57 log A
58
¯
log
peak
theory+𝒞=
2/5
10
Andrea Mitridate, Jonathan Nay, Priyamvada
Natarajan, 10 Cherry Ng, David
J. Nice,thFigure 4. Same as Fig. 3 but for a di↵erent
13selection of models and showing a larger
59 frequency range. The solid lines represent
60
61
18(cf. Kitajima,
YT,
Yokoyama,
Yoo ‘21) Benetge B. P. Perera, Polina Petrov,
median GWB
spectra forOcker,
a subset of new-physics
models D.
(see Appendix
B for more details);
the gray violins
toStella
Koch
Ken
Olum,
TimothyT.correspond
Pennucci,
the posteriors of an HD-correlated free 18
spectral reconstruction of the NANOGrav signal; and62the shaded regions indicate the Figure 7.
63 Same as in Fig. 6 but
41 for the sigw-delta (left panel)64and sigw-ga
power-law-integrated(Thrane & Romano2013) ofA.
variousexisting and planned GWScottinterferometer M.
experiments:
Nihan sensitivity
S. Pol,Henri
Radovan,Ransom,
Paul
S.
Ray,
JosephD.
Romano,labeled fPBH = 1 in the32right panel indicate the PBH32
bound
LISA (Amaro-Seoane et al. 2017), DECIGO (Kawamura
et al. 2011), BBO (Crowder & Cornish 2005),65
Einstein Telescope (ET; teal contour lines 65
3
Punturo et al. 2010),
CosmicExplorer (CE; Reitze etAnn
al. 2019), the
HLVK detector network (consisting ofCarl
aLIGO in Hanford
ShashwatC.
Sardesai,
Schmiedekamp,
Schmiedekamp,
Kai
Schmitz,
TobiasSchröder,
Appendix
C.2
shows
extendedversions
of
the
two
plots
that
includeas(Aasi
DMet al.—2015),
Yuichiro
TADA
3. PBH and Inflation
33 /37 the SMBH
and PBH
Livingston
aVirgo (Acernese
et al. 2015), and KAGRA (Akutsu et al. 2019)) at design sensitivity, andPulsar Timing Array
QCD effect f ∼ nHz ↔ T ∼ 100 MeV

Abe, YT, Ueda ’20, Abe, YT ’23
cf. EPTA ‘23

0.32
0.30

ΩGW = Ωyrβ

0.28

( fyr−1 )
f

0.26
0.24

𝒫ζ = Aζ

w
c2s
10-5

0.001

0.100
10
T [GeV]

0.020

1. × 10-8-9

5. × 10

can’t reach β = 3RDAtal & Domènech ‘21

0.010

0.005

1. × 10-9
5. × 10-100.0Θ(kmax − k)

kmax = 108 Mpc-1

105

QCD

Aζ

Ωyrh2

5. × 10-8

1000( kyr−1 )
k

0.5

1.0

PBH as DM — Yuichiro TADA

1.5
β

2.0

2.5

3.0

0.0

0.5

1.0

1.5

2.0

2.5

ns - 1

3. PBH and Inflation

34 /37

One-loop on CMBRESCEU-20/22

2211.03395

Ruling Out Primordial Black Hole Formation From Single-Field Inflation
Jason Kristiano1, 2, ⇤ and Jun’ichi Yokoyama1, 2, 3, 4, †1

Research Center for the Early Universe (RESCEU),(3) School of Science, The University of Tokyo, Tokyo 113-0033, Japan
Graduate2
Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
3
Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU),
1−loop
WPI, UTIAS, The University of Tokyo, Kashiwa,
Chiba 277-8568, Japantree
4
Trans-Scale Quantum Science Institute, The University
CMBTokyo 113-0033,
ζ of Tokyo,ζ Japan CMB(Dated: August 15, 2023)
CMB

S [ζ]

[hep-th] 14 Aug 2023(k

) ∼ Δ𝒫(k)

k

The most widely
PBHstudied formation mechanism of a primordial black hole (PBH) is collapse oflarge-amplitude perturbation on small scales generated in single-field inflation. In this Letter, we
calculate one-loop correction to the large-scale power spectrum in such a model. We find models
producing appreciable amount of PBHs induce nonperturbative coupling on large scale probed bycosmic microwave background radiation. We therefore conclude that PBH formation from cosmological−1
perturbation theoryζ in single-field inflation is ruled out.

Separate U. assumption
ζ

≫

k

𝒫

H

- ζ as NG boson of asymptotic dilatation(e.g. Assassi, Baumann, Green ‘12)

(classically)ζ is flat
conserved
Primordial black holes (PBHs) have been a research
If the xinflaton passes
through an soft
extremely
regioninterest for more than 50 years [1–3], although
thereof
the potential
with dV /d ⇡ 0 after the comoving
scales2
2 has22ζ(0)2(Lyth,
Malik,
Sasaki ‘05)
ds
=
−
dt
+
a
(t)e
dx
been no observational evidence for them. They could
probed by CMB have left the horizon, it may produce
2
Maldacena’s
consistency(‘03)
be light enough for Hawking radiation to belarge-amplitude
fluctuations
on smallscales. In thisrelation
re= important− dt 2 + ax2(t)dx̃
[4], they are a potential dark matter candidate [5–14]
gion, slow-roll condition fails, and the inflation goes into ad𝒫ζ(kS)(reviewed in [15, 16]), and they can explain LIGO-Virgo
temporary ultraslow-roll(USR)period[104–108].
Dur(3)⟨ζkLζofkSfluctuations,ζkS⟩ ∝ 𝒫ζ(kL)
gravitational wave events [17–22].
ing this regime the non-constant mode
d
ln
k
S
which
would
decay
exponentiallyinSRinflation,
actually
A number of formation mechanisms
of PBHs in the−1
kCMB
grows, as observed in other models [81, 109],
resultinginmerelyscale-redefinition
early Universe has been proposed.
The most well-studied
enhanced power spectrum on specific scales. This may
one makes use of quantum fluctuations [23–26] generalso imply the importance of quantum e↵ects as we willated in cosmic inflation [27–29]. Observations of CMB
PBH as DM — Yuichiro TADA
3.seePBH
and Inflation
35 /37
below.

-

-

S [ζ]

Loop Cancellation
YT, Terada, Tokuda ‘23

tensor ver. (Ota, Sasaki, Wang ’22 x 2, ’23) didn’t vanish……
KY

d
(3)
4
S [ζ] = d x 𝒪bulk + 𝒪surface
[
]
∫
dt

Maldacena’s CR

kPBH

kCMB

∝ 𝒫ζ(kCMB)

kPBH

cf. Arroja & Tanaka ‘11

d𝒫ζ(kPBH)
d ln kPBH

Self-energyiε prescription 10−9d𝒫ζ(q)≫

kCMB

Ward—Takahashi of Asymptotic Dilatationqtree ζ conservation
PBH as DM — Yuichiro TADA∼

∝ 𝒫ζ(kCMB) d ln q
= 𝒫ζ(kCMB)(𝒫ζ(k → ∞) − 𝒫ζ(k → kCMB))∫d ln qMaldacena’s CR

self-energy cancellation

3. PBH and Inflation

36 /37

Summary
1.

Sub-Solar PBHs may be detected

2. Asteroid PBH-DM can be checked by induced GW
w/ LISA & DECIGO
Many theoretical progresses