Inflation, Primordial Black holes and Gravitational Waves

-- Dawn of Gravitational Wave Astronomy --

Misao Sasaki

Yukawa Institute for Theoretical Physics, Kyoto University

IPMU colloquium 24 January, 2018

Inflation

2

Inflation is a quasi-exponential expansion of the Universe at its very early stage; perhaps at t~10-36 sec.

It was meant to solve the initial condition (singularity, horizon &

flatness, etc.) problems in Big-Bang Cosmology: if any of them can be said to be solved depends on precise

definitions of the problems.

Quantum vacuum fluctuations during inflation turn out to play the most important role. They give the initial condition for all the structures in the Universe.

Cosmic gravitational wave background is also generated.

Brout, Englert & Gunzig ’77, Starobinsky ’79, Guth ’81, Sato ’81, Linde ’81,…

What is Inflation?

3

4

2 2 2 2

3

1

( )( ) ;

( ) sinh

ds dt a t dH

a t H Ht

温故知新 (learning from the past)

Creation of Open Universe!

Now in the context of String Landscape

From inflation to bigbang

After inflation, vacuum energy is converted to thermal energy (called “re”heating) and hot Bigbang Universe is realized.

ρ

inflation

Reheating : Γ = H

tf

(birth of hot bigbang universe)

inflation

oscillation

V(f)

tR

f

t

oscillation (MD) RD

5

log L

log a(t)

L=H-1

Size of the Observable Universe

Inflationary Universe Hot Bigbang Universe

length scales of the inflationary universe

L=H0-1

1028cm

108cm LIGO band

~ 46 e-folds

targets for multi-frequency GW astronomy

6

Reheating stage

(102~107(?)cm)

7

Zero-point (vacuum) fluctuations of f :

222

20 3 ;

() ( )

)(k k k

kt

tH t

af f f

( ) ik x

kk

t ef f

harmonic oscillator with friction term and time-dependent

Mukhanov & Chibisov ’81, ….

Quantum fluctuations during inflation

fk

fk

fk

time

kf const.

··· frozen when < H

(on superhorizon scales)

tensor (gravitational wave) modes also satisfy the same eq.

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from f to curvature perturbation

t

xi

0

0f

0

0f

• Inflation ends/damped osc starts on “comoving” (f =const.) 3-surface.

end of inflation

hot bigbang universe

const., 0cT

0ff f vacuum fluctuation:

c f

Hf

f • On f =const. surface, curvature perturbation appears

• Rc gives rise to gravitational potential perturbation Y : 3

5cY

• Photons climbing up from gravitational potential well are redshifted.

Y

Eemit

Eobs obs

emit

emit

1( ) ( )TT

n xT T

Y

• In an expanding universe, this is modified to be emit

1

3( ) ( )

Tn x

T

Y

Sachs-Wolfe effect

• There is also the standard Doppler effect:

( ) ( )emit

Tn n v x

T

For Planck distribution,

c=1 units

d

0

emit line of sight;x nd n

CMB temperature fluctuations

9

Planck CMB map

10

Planck 2013

0

1small corrections

3(T n v T

Y

)

02 73.T K

but important!

Gravitational Waves from Inflation

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Cosmological GWs

scalar field(s) produce density fluctuations -> CMB temp+E-mode fluctuations

E-mode (even parity) B-mode (odd parity) = cannot be produced from density fluctuations

tensor (GW) fluctuations -> CMB temp+E-mode+B-mode fluct’ns

http://www.skyandtelescope.com/ Source: Harvard-Smithsonian Center for Astrophysics

12 CMB B-mode=cosmological GW detector

Planck constraints on inflation

scalar spectral index: ns ~ 0.96

tensor-to-scalar ratio: r < 0.1

simplest model is almost excluded

( )

( )

T

S

P kr

P k

3log[ ( )]1

log

Ss

d k P kn

d k

2V f

Planck 2015 XX

2V f

some element of non-canonicality needed 13

14

GWs from “Standard” Inflation

http://arxiv.org/abs/1206.2109

maybe yes… or maybe just impossible…

could direct detection by GW observatories possible?

blue-tilted GW spectrum?

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possible e.g. in massive gravity inflation model Lin & MS (2015)

tensor (=GW) spectral index:

tensor mass

4

22 5 10inf .

H

H

410 M

quantitative examples

16

2 2 22exp[ ( / ) ]g plm Mf f with

Starobinsky model

22

2g

pl

mM

f

74 8 10.

low-scale model 410inf

8 410 1 5 10GeV, .M

481 4 10GeV, .M

2 2 31 210

2 3end , ,V M H M Mf

with

210 M

2

2 23 61

4 3exppl

pl

V M MM

f

Kuroyanagi, Lin, MS & Tsujikawa ’17

Big-Bang Nucleosynthesis (BBN) gives stringent constraints

93 10E GeV

133 10E GeV1510E GeV

Gravitational Wave Physics/Astronomy

17

18

The Dawn has arrived!

GWs from binary BH merger were detected for the first time on Sep14, 2015 (GW150914).

LIGO

BBH masses: 36 𝑀⨀+ 29 𝑀⨀

Source redshift: 0.09 (~ 1.2 Glyr)

Event rate: 0.6-12 /Gpc3 /yr

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Unusual properties of LIGO BHs

They seem to be unusually heavy! (exc. GW151226)

LIGO has detected 4BBH mergers (+1 candidate) so far.

20 𝑀⨀

Their spins seem to be unusually small!

Any implications ?

ceff would be larger if astrophysical origin

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eff =1 1 2 2 1 2( ) : /L Lm m m m Lc s s n n L

LIGO BH spins

ceff =0 is consistent (exc. GW151226)

http://www.ctc.cam.ac.uk/

L

GW170814 also consistent with zero

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Network of GW Observatories VIRGO started to operate on 1st Aug. 2017 KAGRA will start operation by 2020-2021 (iKAGRA has started!) LIGO-India has been recently approved by Indian gov.

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Huge advantage in angular resolution

S/N=15 (LIGO), 4.4 (Virgo)

S/N=24

S/N=18.3 (LIGO+Virgo)

• Impressive increase from LIGO alone (2) to LIGO+VIRGO (3) • +KAGRA (4) • +LIGO-India (5)

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KAGRA KAmioka GRAvitational wave detector

In Japanese it is pronounced as Kagura, which means “God Music” （神楽）

Previously called LCGT Large Cryogenic

Gravitational wave Telescope

Arm length 3km Cooled to 20K

Super-Kamiokande

KAGRA APCTP

http://gwcenter.icrr.u-tokyo.ac.jp/en/

KAGRA

YITP

YITP

IPMU

KAGRA

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http://lisa.nasa.gov/

Deci-hertz Interferometer Gravitational wave Observatory

Laser Interferometer Space Antenna

Space-based Future Projects

DECIGO: 1,000 km launched by ~2030? target freq: ~ 0.1 Hz

LISA: 5,000,000 km launched by ~2034? target freq: ~10-3Hz

Arm Length

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Multi-frequency GW Astronomy Pulsar Timing Array

Spaced-based

Ground-based

http://rhcole.com/apps/GWplotter/

New window to explore the Unknown Universe!

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Binary Neutron Star merger found!

GW170817 / GRB170817A

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multi-messenger astronomy!

70 observatories include. 7 satellites

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Cosmological Implication!

from just a single event!

Primordial Black Holes

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What are Primordial BHs?

PBH = BH formed before recombination epoch (ie at z>>1000)

Hubble size region with r/r=O(1) collapses to form BH

Such a large perturbation may be produced by inflation

PBHs may dominate Dark Matter.

Origin of supermassive BHs (𝑀 ≳ 106𝑀⨀) may be primordial.

Carr (1975), ….

Carr & Lidsey (1991), …

Ivanov, Naselsky & Novikov (1994), ...

conventionally during radiation-dominated era

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Curvature perturbation to PBH

𝐻−1 = 𝑎/𝑘

If , it collapses to form BH

𝑀PBH ∼ 𝜌𝐻−3 ∼ 105𝑀⊙

𝑡

1𝑠∼ 20𝑀⊙

𝑘

1pc−1

−2

Spins of PBHs are expected to be very small

3 2

2

4 8

3

( )

c c

GR

a

r

22

2

cc

kH

a

r

r at

Hamiltonian constraint (Friedmann eq.)

3 2 1 ( ) ~~ cR H r r Young, Byrnes & MS ‘14

3 2( ) ~R H3 0( )R

2 36 16( )( , ) ( , ) ( , )H t x R t x G t x r

gradient expansion/separate universe approach

examples

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hybrid-type inflation

C grows near the saddle point

non-Gauss may become large

non-minimal curvaton

2 2

1

2

1

2

( )

( )

L f g

h m

f c c

f c

Garcia-Bellido, Linde & Wands ‘96, … Domenech & MS ‘16

Abolhasani, Firouzjahi & MS ’11,..

Pattison et al. 1707.00537

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Accretion to PBH?

Bondi accretion

24 1 3 : / / ,B s sM r c c Pr r 21 , ( )~B

s

GMr

cO

23

3143

4 3 2 : ,sM M

s M

M M M

c aM H HM c H

HM G HH H a

r

horizon size at the time of PBH formation

3

8Ma

M daM

H a

PBH mass can increase by a factor of 1.5 at most

Mass increase can be ignored, given other ambiguities

• accretion rate/Hubble time

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Effect on CMB?

• Eddington luminosity: max luminosity from accretion

4edd ;

p

T

GMm cL

= proton mass

= Thomson cross section

p

T

m

3

4 4edd p pPBHR PB

PH

R R R T eq T eq

BH

Gm Gmn L a

H H Hf

a H

r r

r r r

1edd ;L L

3

410 ; PBHPBH PBH

CDMeq

a

af f

small, but may not be entirely negligible…

accretion can lead to radiative emission

• energy output/Hubble time

luminosity from PBH …

Constraints on PBHs

f

PBHPBH

DM

Can DM be PBHs?

Ali-Haimoud & Kamionkowski, 1612.05644

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Ricotti, Ostriker & Mack (’08) overestimated the accretion effect

window at 1021-1023g

Inomata et al., 1711.06129

LIGO BBHs may occupy ~10% of DM

LIGO BHs = PBHs?

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MS, Suyama, Tanaka & Yokoyama ‘16

fraction of PBH in dark matter 𝟏𝟎−𝟒

LIGO

eve

nt

rate

[G

pc-3

yr-1]

3-body interaction leads to formation of

BH binaries

𝟏𝟎−𝟐 𝟏𝟎−𝟑

2 2

120 20PBH

kM M M

T

100MeV

kpc

tightest constraint at

PBH merger rate

10~M M

(cf. Ali-Haïmoud et al., 1709.06576)

f

f

testing PBH hypothesis

37

Nakamura et al. PTEP 2016 (2016) 093E01

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testing PBH hypothesis 2 Kocsis, Suyama, Tanaka, Yokoyama, arXiv:1709.09007

BBH Merger Rate at time t:

1 2 1 2 1 2intr , ,( ) ( ) ( ) :t tP m m t g m g m m m m m

36 22

37 21 • PBH binary scenario

• Dynamical formation in dense stellar systems 4

O'Leary et al (2016)

mass function

intrinsic probability

clearly distinguishable!

log L

log a(t)

L=H-1

Size of the Observable Universe

Inflationary Universe Hot Bigbang Universe

testing inflation by GW astronomy

L=H0-1 1028cm

<1010cm testing MG?

Reheating stage

1018cm LIGO PBHs

CMB B-modes

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PBH formation

Inflation has become the standard model of the Universe.

further tests are needed to confirm inflation.

Cosmological GWs are the key to understanding/confirmation of inflation.

LIGO detection of GWs marked the 1st milestone in GW physics/astronomy.

The Dawn has arrived!

LIGO BHs may be primordial.

advanced GW detectors will prove/disprove the scenario.

Multi-frequency GW astronomy/astrophysics has begun.

Summary

GWs will be an essential tool for exploring the Physics of the Unknown Universe

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