Inflation, Primordial Black holes and Gravitational Waves · 2018-01-26 · Inflation is a...
Transcript of Inflation, Primordial Black holes and Gravitational Waves · 2018-01-26 · Inflation is a...
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
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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
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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
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Reheating stage
(102~107(?)cm)
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Zero-point (vacuum) fluctuations of f :
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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
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Planck CMB map
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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
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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
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22 5 10inf .
H
H
410 M
quantitative examples
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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
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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
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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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