primordial black holes from inflation and gravitational waves · 20190128 · primordial black...
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Primordial Black holes from Inflation and
Gravitational Waves
Misao Sasaki
Kavli IPMU, University of Tokyo
TG2019 SFU, Vancouver
24 Jan. 2019
Inflation & PBH formation
2
3
cosmic spacetime diagram
a/k0
aend a0
Rad. dom. 1/Hr ~a2
aeq
Matt. dom. 1/Hm ~a3/2
Inflation Hinf ~ 105MPl
???
log L
N= log a
1/H0
current Hubble radius
constant
comoving
scale
ç???
“reheating”
0~ 10~ 60~ 120
aini
( = lnHinf
H0 ) ~ 30
a(1GeV)
4
curvature perturbation from inflation• inflaton (~massless) vacuum fluctuations (=Gaussian)
2 2 1 2
, ~ ;kiw tk k k
k
kk e w Haw
φ ϕ ϕ −= =!
≫
rapid expansion renders oscillations frozen at k/a < H (fluctuations become “classical” on superhorizon scales)
22
3
22 / ~
~ ;k kk a H
H k HHak
ϕ δφπ
⎛ ⎞⇒ = ⎜ ⎟
⎝ ⎠≪
• curvature perturbation on comoving slices
··· conserved on superhorizon scale for singlefield slowroll models
··· almost scaleinvariant
ℛc = −H·ϕ
δϕ
(almost scaleinvariant if is also slowly varying)·ϕ
ϵ = −·H
H2≪ 1for
5
observational constraint on inflationPlanck 2015 results XX
powerlaw piecewise continuous (9 segments)𝒫ℛ = A(k /k*)ns−1
ns ≈ 0.968 ⋯ almost scaleinvariant
6
Planck constraint
There are some constraints on small scales, but quite weak.
Bringmann et al., arXiv:1110.2482
constraints on small scales are from BHs
observational constraint on inflation
disappears if CDM = WIMP
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No resolution to say anything precise about higher k.
?
Bayesian reconstruction of the primordial power spectrum
with l < 2300. (Planck 2015)
8
N= log a
a/k*
a* aend a0aini areentry aeq
a/k0
A peak in the primordial curvature perturbation, which leaves horizon and gets frozen at a*.
Rad.dom. 1/Hr ~a2
log L
1/H0
PBH formation
ç???
k* = Ha*
9
N= log a
a/k*
a* aend a0aini areentry aeq
a/k0
The peak reenters horizon during radiation era.If the amplitude > O(0.1), PBH will form.
Rad.dom. 1/Hr ~a2
log L
1/H0
ç???
PBH formation
k* = Ha*
10
a/k*
a* aend a0aini areentry aeq
a/k0
Rad.dom. 1/Hr ~a2
PBH mass:
Inverse relation:
log L
1/H0
N= log a
1N
a/k*
a* aend a0aini areentry aeq
a/k0
Rad.dom.1/Hr ~a2
Nosi
PBH mass:
Inverse relation:
The formation of Primordial Black
Holes
log L
1/H0
N= log a
1 1
22 58 0 875810 10 .
PBH HN NM
M M M e MH
J PlPl Pl
1N
1N
11 6
144 42 10
. lnNM§ ·
¨ ¸© ¹
PBH
g
a/k*
a* aend a0aini areentry aeq
a/k0
Rad.dom.1/Hr ~a2
Nosi
PBH mass:
Inverse relation:
The formation of Primordial Black
Holes
log L
1/H0
N= log a
1 1
22 58 0 875810 10 .
PBH HN NM
M M M e MH
J PlPl Pl
1N
1N
11 6
144 42 10
. lnNM§ ·
¨ ¸© ¹
PBH
g
ç???
PBH mass scale does NOT depend on the reheating
physics
PBH formation
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 δρ/ρ=O(1) collapses to form BH
Such a large perturbation may be produced by inflation
PBHs may dominate Dark Matter.
Carr (1975), ….
Carr & Lidsey (1991), …
Ivanov, Naselsky & Novikov (1994), ...
conventionally during radiationdominated era
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Supermassive BHs may originate from PBHs.(M ≳ 106M⊙)….
Bean & Magueijo (2002), ...
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Curvature perturbation to PBH
If , it collapses to form BH
Spins of PBHs are expected to be very small
Hamiltonian constraint (Friedmann eq.)
( )3 2 1 ( ) ~~ cR H δρ ρ⇔ /Young, Byrnes & MS ‘14
3 2( ) ~R H3 0( )R !
2 36 16( )( , ) ( , ) ( , )H t x R t x G t xπ ρ+ = + ⋅ ⋅ ⋅
gradient expansion/separate universe approach
R(3) ≈ −4a2
∇2ℛc ≈8πG
3δρc
δρc
ρ≈ ℛc
k2
a2= H2at
examples
14
hybridtype inflation
CR grows near the saddle point nonGauss may become large
nonminimal curvaton
2 2
12
12
( )
( )
L f g
h m
µνµ νφ χ χ
φ χ
= − ∂ ∂
−
GarciaBellido, Linde & Wands ‘96, … Domenech & MS ‘16
Abolhasani, Firouzjahi & MS ’11,..Pattison et al. 1707.00537
LIGO BHs = PBHs?
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MS, Suyama, Tanaka & Yokoyama ‘16
fraction of PBH in dark matter
LIGO ev
ent
rate
[G
pc3yr
1]
3body interaction leads to formation of
BH binaries
2 2
120 20PBHkM M M
T
−
−
⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟
⎝ ⎠⎝ ⎠⊙ ⊙" "
100MeVkpc
tightest constraint at
PBH merger rate
10~M M⊙(cf. AliHaïmoud et al., 1709.06576)
ff =
testing PBH hypothesis
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Nakamura et al. PTEP 2016 (2016) 093E01
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testing PBH hypothesis 2Kocsis, Suyama, Tanaka, Yokoyama, arXiv:1709.09007
BBH Merger Rate at time t:
1 2 1 2 1 2i n t r , ,( ) ( ) ( ) :t tP m m t g m g m m m m mα∝ = +
36 2237 21
α< <• PBH binary scenario
• Dynamical formation in dense stellar systems 4α ≈
O'Leary et al (2016)
mass function
intrinsic probability
clearly distinguishable!
PBH constraints: recent update
1015 1020 1025 1030 1035
MPBH [g]
105
104
103
102
101
f=
PB
H/
DM
BH
Eva
por
atio
n
FemtoKepler
CMBEROS/MACHO
HSC M31 constraint (95% limit)
1015 1010 105 100MPBH [M]
Figure 5 The redcolor shaded region show the 95% C.L. upper bound on the PBH mass fraction to DMin the halo regions of MW and M31, derived from our microlensing search of M31 stars based on the“onenight” HSC/Subaru data. To derive this constraint, we took into account the effect of finite sourcesize assuming that all source stars in M31 have a solar radius (see text for details). The effect weakensthe upper bounds at M < 107M. Our constraint can be compared with other observational constraintsas shown by the gray shaded regions: extragalactic rays from PBH evaporation [32], femtolensing ofray burst (“Femto”) [33], microlensing search of stars from the satellite 2years Kepler data (“Kepler”)[18], MACHO/EROS/OGLE microlensing of stars (“EROS/MACHO”) [15], and the accretion effects onthe CMB observables (“CMB”) [34], updated from the earlier estimate [35].
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Niikura et al. ‘1701.02151v2
microlensing
λopt > RSch(MPBH)wave effect:
MPBH ≈ 1020 − 1023g Treentry ~ 102 103 TeV
if LIGO BHs=PBHsMS, Suyama, Tanaka, Yokoyama ‘16
window only at
for ~5 yrs obs
PBHs = CDM?
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monocromatic PBH production
End of the 1st stage of inflation
ℒ = R +R2
6M2−
12
(∂χ)2 − V(χ)
χ
R2inflation
Pi, Zhang, Huang & MS ‘18
f ≈ 0.73
sharp peak
sharp peak in P(k) spike in f
spike
f ≡ΩPBH
ΩCDM∝ exp [−
1𝒫(k) ]
μ2 ≈H2
2nd
H21st
21
μ = 8
Zhang, Hwang, Pi & MS ‘18
• nonnegligible PBH formation means
• GWs are produced with amplitude:
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2nd order GWsSaito & Yokoyama ’09, Alabidi et al. ’13, …
𝒫S(k) ≳ 10−2.5
··hij + 3H ·hij − a−2Δhij = Sij
Sij =1a2
∂iℛc∂jℛc + ⋯ ∼k2
a2𝒫S(k)
hij ∼k2
a2H2𝒫S(k) ∼ 𝒫S(k) 𝒫GW(k) ∼ (𝒫S(k))2
2nd order GWs could dominate GW background at f>1010 Hz (k>104 Mpc1)
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352
Fig. 1. Top: The energy density of the induced GWs for the power spectrum for a peak width, ∆ =0.0, 1.0 × 10−3, 1.0 × 10−1, 1.0. Bottom: Energy density of scalarinduced GWs associated with PBHformation together with current pulsar constraint (thick solid line segment) and sensitivity of variousGW detectors (convex curves). Solid wedged lines indicate the energy density with the parameters(ΩPBHh2, MPBH) = (10−5, 102M⊙) (left), (10−1, 1020g) (right) for sufficiently small ∆ (thick lines) and∆ = 1.0 (thin lines).
Downloaded from https://academic.oup.com/ptp/articleabstract/126/2/351/1838316by gueston 14 July 2018
GWs test PBH scenarios!
Saito & Yokoyama,arXiv:0912.5317
(ΩPBHh2, MPBH) = (10−5,100M⊙)(ΩPBHh2, MPBH) = (10−1,1020g)
NonGaussianity Effect?
14
12
10
8
6
4
2
ℛ(x) = ℛg(x)
RG Cai, S Pi & MS, arXiv:1810.11000
PBH constraints:If PBHs=CDM LISA must detect induced GWs!
MPBH = 1022 g
fGW= 3
×103 Hz
fGW= 3
×102 Hz
AR=102
AR=103
AR=104
 


()
(
)
fGW= 3
×103 Hz
fGW= 3
×102 Hz
AR=102
AR=103
AR=104
 


()
(
)
k3
FNL=0
FNL=10
FNL=20
FNL=50



/
Ω
+FNL [ℛ2g(x) − ⟨ℛ2
g(x)⟩]
log L
log a(t)
Size of the Observable Universe
L∝a(t)
Inflationary Universe Hot Bigbang Universe
probing inflation by GW astronomy
k=const.
L=H01~1028cm
~1011cm
Reheating stage
~1018cmLIGO BHs?
CMB Bmodes
25
PBH formation?
physics at N ~ 20  40physics at
N ~ 60
L=H1
CDM BHs?
∗ Inflation has become the standard model of the Universe. further tests are needed to confirm inflation.
∗ Inflation can produce large curvature perturbation on small scales. PBHs are virtually the only probe on very small scales.
∗ LIGO BHs may be primordial. future GW detectors(+G lensing) will prove/disprove the scenario.
∗ CDM can be dominated by PBHs of M~1020g. secondary GWs may be detected by future GW detectors.
∗ Multifrequency GW astronomy/astrophysics is arriving!
Summary
GWs will be an essential tool for proving/falsifying PBH scenarios
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