Gravitational waves
in the inhomogeneous Universe
Masamune Oguri
RESCEU/Physics/Kavli IPMU
University of Tokyo

2019/9/3 Cosmological Frontiers in Fundamental Physics@Perimeter

Plan of this talk• standard siren without redshift info with crosscorrelation approach[MO Phys. Rev. D 93(2016)083511]• effect of gravitational lensing on the distributionof binary black hole mergers[MO MNRAS 480(2018)3842]

Gravitational waves (GW)

• observed for the

first time in 2015

• mergers of compact
binaries such as
black hole (BH) andneutron star (NS)• very useful probe
R. Hurt/Caltech-JPL/EPA

of cosmology andastrophysics!

Gravitational wave standard sirens• we can infer mass (→GW amplitude) of inspiraling
compact binary from the waveform• by comparing with observed amplitude, we canmeasure luminosity distance (incl. H0) directly(Schutz 1986)

louderless loudIEW LETTERS
Abbott+2016

week ending
12 FEBRUARY 2016

Inspiral

h/

5/3
Mz

DL (z)f

2/3

5/3 11/3
˙
f / Mz f→ chirp mass Mz
and distance DL
analytic
numerical analytic(post-Newtonian) relativity (QNM)

Redshift information• standard siren can constrain H0 and othercosmological parameters if the redshift is known• usually detection of EM counterpart and/or
host galaxy is needed for the redshift

localization• this is challenging because of the poor2
accuracy (currently >10−100 deg )Abbott+2017

GW170817 (NS-NS merger)

urnal Letters, 848:L12 (59pp), 2017 October 20

Abbott et al.

3easurement of the GW polarization is cruinferring the binary inclination. This in, ◆, is defined as the angle between theight vector from the source to the detecthe orbital angular momentum vector ofy system. For electromagnetic (EM) pheit is typically not possible to tell whether as orbiting clockwise or counter-clockwise
valently, face-on or face-off), and sources
efore usually characterized by a viewing
the gravitational-wave,
The left panel showsan orthographicmin(◆, 180 gamma-ray,◆).and optical
Bysignals.
contrast,
GW
mea-projection of the 90% credible regions fromeen), the initial LIGO-Virgo localization (31 deg ; dark green), IPN triangulation from the time delay between Fermi and INTEGRAL (lightdark blue). The inset shows the location of the apparent host galaxy NGC 4993 in the Swope optical discovery image at 10.9 hr after thets
canidentify
thedays sensetherotation,e DLT40
pre-discovery
image from 20.5
prior to mergerof(bottomright). The
reticle marks the position of the transient in both images.
gamma-ray
bursts (GRBs)
and
by subsequent sGRB discoveries◆ rangesfromwere0discovered(counter-clockwise)to (see theet al.compilation
GW170817 measurement of H0 . Marginal, and their cosmic origin was ﬁrst establishedanalysis by Fong et al. 2015 and also TrojaFigure2016).1.
Neutronstar detections
binary mergers are byalso expected, however, to produce(1973).
GRBs are classiﬁedPrevious
as long or short, GW(clockwise).
ized(i)posterior
isotropic electromagnetic signals, which include
early optical density for H0 (blue curve). Constraints
on and spectral hardness(Dezalay et al. 1992;
infrared emission, adisso-called kilonova/macronova (hereafter
993). large
Uncoveringuncertainties
the progenitors of GRBs in andadluminosity
1-Rosswog
and 2005;
2 from Planck (Planck Collaboration et al.
kilonova; Li & Paczyński 1998; Kulkarni at
2005;
key challenges in high-energy astrophysics
Metzger et al. 2010; Roberts et al. 0
2011; Barnes & Kasen 2013;2007). It has long been2016) and SHoES (Riess et al. 2016) are shown in
dt Ramirez-Ruiz
inclination(Abbottetal.
2016a)
becauseKasen et al. 2013; Tanaka & Hotokezaka 2013; Grossman et al.
GRBs might be related to neutron star
2014; Barnes et al. 2016; Tanaka 2016; green
Metzger 2017)
due orange.
to1986; Paczynski 1986; Eichler et al. 1989;
and
The maximum a posteriori value
LIGO
detectors
thatwereinvolved
areradioactive decay of rapid neutron-capture process (r-process).
nuclei(Lattimer & Schramm 1974, 1976)
synthesizedin 68.3% credible interval from this PDF isof short gamma-ray burst (sGRB) studies
andminimalo-aligned,
preventingaprecisepolarizadynamical and accretion-disk-wind ejecta during the merger;
hrough (for reviews see Nakar 2007; Berger+12.02• GRB and kilonova detected, host galaxy identified• first constraint on H from gravitational waves
1

Future?

• kilonova is faint (~24 mag @ 400 Mpc)
GRB observed only on-axis• short(e.g., Dalal+2006, Nissanke+2010)• what about BH-BH mergers?
standard siren without redshift?

MO Phys. Rev. D93(2016)083511

Cross-correlation approach• idea: constrain distance-redshift relation withcross-correlation of GW sources (known DL)
and galaxies (known z)• similar to “clustering redshift” (e.g., Newman 2008)• no follow-up of GW sources neededCross-correlation approach• cross-correlation of
spatial distributions

GWs
galaxies

00~~~w(✓) = h GW (✓ ) gal (✓ + ✓)i• when Dobs > D(zgal)
cross-correlation is
small

Dobs

D(zgal)w(θ)θθ

Cross-correlation approach• cross-correlation ofgalaxies

GWs

spatial distributions

0
0
~
~
~
w(✓) = h GW (✓ ) gal (✓ + ✓)i• when Dobs ≈ D(zgal)
cross-correlation is
large

Dobs

D(zgal)w(θ)θθ

Cross-correlation approachgalaxies• cross-correlation of
spatial distributions

GWs

0
0
~
~
~
w(✓) = h GW (✓ ) gal (✓ + ✓)i• when Dobs < D(zgal)
cross-correlation is
small

Dobs

D(zgal)w(θ)θθ

Gravitational lensing as noise
y
a
r
t
ligh

sourceobs
lens (dark matter+baryon)(GW)• gravitational lensing magnification µ changes
the observed luminosity distance
h
i
1/2
~ z)
Dobs = D̄µ⇡ D̄ 1 (✓,Apparent clustering due to lensing• lensing depends onsky position

Dobs=const

D=const• induces additional
clustering patternon the skyχ2χ ranges between diﬀerent redshift bins, and bg
0 there is no overlap
med thatof redshift
at there is no overlap of redshift ranges between diﬀerent
redshiftbins, and bg is the
MO Phys.
Rev. D93(2016)083511
hespectroscopic
galaxies.
overlap ofgalaxies.
redshift ranges between diﬀerent redshift bins, and bg is the bias
troscopic
der the cross-correlation between the GW sources and the spectroscopic galaxies. Fromies.
e cross-correlation between the GW sources and the spectroscopic galaxies. From Eq. (8)e cross-correlation
power
spectrumion
between the GW
sourcesand theasspectroscopic galaxies. From Eq. (8), we
correlation power spectrum as
wer spectrum as
wi gj
si gj
ti gj
C
(ℓ)
=
C
(ℓ)
+
C
(ℓ)
wi gj
si gj
ti gj
(ℓ)t=
C (ℓ) + C (ℓ)
wi gj
si gC
j
i gj
C
(ℓ) = C (ℓ)!+ C (ℓ)
(18)
"
#
∞
"
#1/2
!
H(z)
ℓ
+
∞
g
s
g
s
i
j
"H(z)(z)# bGW bℓg+
physicalspatial! ∞ si gj C
1/2
dz Wgi (z)W
(ℓ) =
P
;
z
m
s
H(z)
W0 i (z)Wj (z) ℓ j2+ 1/2
C (ℓ)s = g dz
bGWχb2g Pm;z χ
correlationdz Wi (z)Wj 0(z) 2 bGW bg Pm χ
=
;z
(19)
χ
χ
0
"
#
! ∞ χ
! z
′
")
#1/2 ′
!
! zt
ℓ
+
H(z
g "
′
tj gj! ∞′′κ′ℓbg+Pm
1/2 ′
)z) #
;z
(ℓ)
(z
;
z =
g dz
′′ Wjκ (z′ )W H(ztj gj Ct dz Wi (z)′ H(z
′2
′
ℓ
+
1/2
)
;z χ
(ℓ) =
dz Wi (z)dz W (z )W (z ; z) ′2 bg′ Pχm
′
′
(20)
;
z
dz Wit (z) 0 dz ′ Wjg0(z)W κ0(z ′ ; z) 0j ′2 bg Pm
4 χ
χ
′
χ
χ
apparent
duepower
to weaklensing0
si gjclustering
tj gj
si gj
ar power spectrum for Pm (k; z) in sboth
C
and
C
.
The
spectrum
C
com
g
t
g
s
g
i j
j j
i j
er spectrum for Pm (k;and C. The power
comes fromsi gjz) in both
tj gj Csi gj spectrum C
P
(k;
z)
in
both
C
and
C
.
The
power
spectrum
C
comes
from
the
z distributions. On. (8)the other hand,Cm and represents the physical correlation of spatial
tj gj
d represents
the physical correlation of spatial distributions. On the
other
hand,
C
,
w
esecondphysicalcorrelationof spatialother
hand,eﬀect
C tj gj on, whichtermof Eq. (8),is the distributions.
correlation of On
thetheweaklensingluminosity dista
term of Eq. (8), is the correlation of the weak lensing eﬀect on luminosity distances of8), is the correlationofthe allweaklensingeﬀect on luminosity
distances of GW
ectroscopic
galaxies.
Since
matterfluctuations
along
the
line-of-sightcontributes
tolenw
opic
galaxies.
Since
allmatterfluctuations
along
the
line-of-sightcontributes
to
weak
1.1
ince all matter
fluctuations along
theluminosity
line-of-sightand
contributes
to weaklensing,
negligible
cross-correlations
betweenredshift
bins
which
are
well
separate
le cross-correlations
betweenandredshiftbinsseparated
which arewith
welleachseparated withtions
between luminosityand luminosity
redshift bins
which
are well

Cross-correlation signals

0.9

zg+0.05zg−0.05χ2
χ ranges between diﬀerent redshift bins, and bg
0 there is no overlap
med thatof redshift
at there is no overlap of redshift ranges between diﬀerent
redshiftbins, and bg is the
MO Phys.
Rev. D93(2016)083511
hespectroscopic
galaxies.
overlap ofgalaxies.
redshift ranges between diﬀerent redshift bins, and bg is the bias
troscopic
der the cross-correlation between the GW sources and the spectroscopic galaxies. Fromies.
e cross-correlation between the GW sources and the spectroscopic galaxies. From Eq. (8)e cross-correlation
power
spectrumion
between the GW
sourcesand theasspectroscopic galaxies. From Eq. (8), we
correlation power spectrum as
wer spectrum as
wi gj
si gj
ti gj
C
(ℓ)
=
C
(ℓ)
+
C
(ℓ)
wi gj
si gj
ti gj
(ℓ)t=
C (ℓ) + C (ℓ)
wi gj
si gC
j
i gj
C
(ℓ) = C (ℓ)!+ C (ℓ)
(18)
"
#
∞
"
#1/2
!
H(z)
ℓ
+
∞
g
s
g
s
i
j
"H(z)(z)# bGW bℓg+
physicalspatial! ∞ si gj C
1/2
dz Wgi (z)W
(ℓ) =
P
;
z
m
s
H(z)
W0 i (z)Wj (z) ℓ j2+ 1/2
C (ℓ)s = g dz
bGWχb2g Pm;z χ
correlationdz Wi (z)Wj 0(z) 2 bGW bg Pm χ
=
;z
(19)
χ
χ
0
"
#
! ∞ χ
! z
′
")
#1/2 ′
!
! zt
ℓ
+
H(z
g "
′
tj gj! ∞′′κ′ℓbg+Pm
1/2 ′
)z) #
;z
(ℓ)
(z
;
z =
g dz
′′ Wjκ (z′ )W H(ztj gj Ct dz Wi (z)′ H(z
′2
′
ℓ
+
1/2
)
;z χ
(ℓ) =
dz Wi (z)dz W (z )W (z ; z) ′2 bg′ Pχm
′
′
(20)
;
z
dz Wit (z) 0 dz ′ Wjg0(z)W κ0(z ′ ; z) 0j ′2 bg Pm
4 χ
χ
′
χ
χ
apparent
duepower
to weaklensing0
si gjclustering
tj gj
si gj
ar power spectrum for Pm (k; z) in sboth
C
and
C
.
The
spectrum
C
com
g
t
g
s
g
i j
j j
i j
er spectrum for Pm (k;and C. The power
comes fromsi gjz) in both
tj gj Csi gj spectrum C
P
(k;
z)
in
both
C
and
C
.
The
power
spectrum
C
comes
from
the
z distributions. On. (8)the other hand,Cm and represents the physical correlation of spatial
tj gj
d represents
the physical correlation of spatial distributions. On the
other
hand,
C
,
w
esecondphysicalcorrelationof spatialother
hand,eﬀect
C tj gj on, whichtermof Eq. (8),is the distributions.
correlation of On
thetheweaklensingluminosity dista
term of Eq. (8), is the correlation of the weak lensing eﬀect on luminosity distances of8), is the correlationofthe allweaklensingeﬀect on luminosity
distances of GW
ectroscopic
galaxies.
Since
matterfluctuations
along
the
line-of-sightcontributes
tolenw
opic
galaxies.
Since
allmatterfluctuations
along
the
line-of-sightcontributes
to
weak
1.1
ince all matter
fluctuations along
theluminosity
line-of-sightcontributes
toweak
lensing,
negligible
cross-correlations
betweenandredshift
bins
which
are
well
separatez+0.05
g
le cross-correlations
betweenandredshiftbinsseparated
which arewith
welleachseparated withtions
between luminosityand luminosity
redshift bins
which
are
well
zg−0.05

Cross-correlation signals

0.9

χ2
χ ranges between diﬀerent redshift bins, and bg
0 there is no overlap
med thatof redshift
at there is no overlap of redshift ranges between diﬀerent
redshiftbins, and bg is the
MO Phys.
Rev. D93(2016)083511
hespectroscopic
galaxies.
overlap ofgalaxies.
redshift ranges between diﬀerent redshift bins, and bg is the bias
troscopic
der the cross-correlation between the GW sources and the spectroscopic galaxies. Fromies.
e cross-correlation between the GW sources and the spectroscopic galaxies. From Eq. (8)e cross-correlation
power
spectrumion
between the GW
sourcesand theasspectroscopic galaxies. From Eq. (8), we
correlation power spectrum as
wer spectrum as
wi gj
si gj
ti gj
C
(ℓ)
=
C
(ℓ)
+
C
(ℓ)
wi gj
si gj
ti gj
(ℓ)t=
C (ℓ) + C (ℓ)
wi gj
si gC
j
i gj
C
(ℓ) = C (ℓ)!+ C (ℓ)
(18)
"
#
∞
"
#1/2
!
H(z)
ℓ
+
∞
g
s
g
s
i
j
"H(z)(z)# bGW bℓg+
physicalspatial! ∞ si gj C
1/2
dz Wgi (z)W
(ℓ) =
P
;
z
m
s
H(z)
W0 i (z)Wj (z) ℓ j2+ 1/2
C (ℓ)s = g dz
bGWχb2g Pm;z χ
correlationdz Wi (z)Wj 0(z) 2 bGW bg Pm χ
=
;z
(19)
χ
χ
0
"
#
! ∞ χ
! z
′
")
#1/2 ′
!
! zt
ℓ
+
H(z
g "
′
tj gj! ∞′′κ′ℓbg+Pm
1/2 ′
)z) #
;z
(ℓ)
(z
;
z =
g dz
′′ Wjκ (z′ )W H(ztj gj Ct dz Wi (z)′ H(z
′2
′
ℓ
+
1/2
)
;z χ
(ℓ) =
dz Wi (z)dz W (z )W (z ; z) ′2 bg′ Pχm
′
′
(20)
;
z
dz Wit (z) 0 dz ′ Wjg0(z)W κ0(z ′ ; z) 0j ′2 bg Pm
4 χ
χ
′
χ
χ
apparent
duepower
to weaklensing0
si gjclustering
tj gj
si gj
ar power spectrum for Pm (k; z) in sboth
C
and
C
.
The
spectrum
C
com
g
t
g
s
g
i j
j j
i j
er spectrum for Pm (k;and C. The power
comes fromsi gjz) in both
tj gj Csi gj spectrum C
P
(k;
z)
in
both
C
and
C
.
The
power
spectrum
C
comes
from
the
z distributions. On. (8)the other hand,Cm and represents the physical correlation of spatial
tj gj
zg+0.05
d represents
the physical correlation of spatial
distributions. On the
other
hand,
C
,
w
esecondphysicalcorrelationof spatialother
hand,eﬀect
C tj gj on, whichtermof Eq. (8),is the distributions.
correlation of On
thetheweaklensingluminosity dista
term of Eq. (8), is the correlation of the weaklensingeﬀect
onluminosity
distances of
z
−0.05
g
8), is the correlationofthe allweaklensingeﬀect on luminosity
distances of GW
ectroscopic
galaxies.
Since
matterfluctuations
along
the
line-of-sightcontributes
tolenw
opic
galaxies.
Since
allmatterfluctuations
along
the
line-of-sightcontributes
to
weak
1.1
ince all matter
fluctuations along
theluminosity
line-of-sightand
contributes
to weaklensing,
negligible
cross-correlations
betweenredshift
bins
which
are
well
separate
le cross-correlations
betweenandredshiftbinsseparated
which arewith
welleachseparated withtions
between luminosityand luminosity
redshift bins
which
are well

Cross-correlation signals

0.9

MO Phys. Rev. D93(2016)083511

Forecast• GWs from 3rd-generation
exp. + galaxies from Euclid(0.3 < z < 1.5)

• lmax is related with accuracyof GW localizations• tight constraints on H0

and w possible with thecross-correlation!

MO Phys. Rev. D93(2016)083511

Cross-correlation: Summary• proposed cross-correlation of GW sourcesand galaxies with known z to constrain H0

and other cosmological parameters• standard siren cosmology without redshift andeven at high-z• other applications of cross-correlation?

− infer progenitor from bias (e.g., Raccanelli+2016)− 3D clustering in distance space (e.g., Zhang 2018)a lot of room to explore!

Origin of binary BHs?

• ~10-30 M⨀ BHs
discovered by
LIGO/VIRGO• their origin still

https://www.ligo.caltech.edu

unknown− Pop-I/II?
− Pop-III?
− PBH?

Models of BH formation
Pop-I/II
Pop-IIIstar/BH
star/BH
formation formation

z~0

z~10

z~30

Primordial
BH
formationz≫1000time• GW observed at z=0 due to long delay timeNakamura+2016; Koushiappas & Loeb 2017

Key observation: high-z eventsd (cumulative event rate / yr) / d ln z

1e+06

predict different
event rates at z ≳15

PBH

1e+05
10000

Pop III BBH
Pop I and II OLD
PBBH

1000

• accessible in 3rdgen. experiments

astrophysicalorigin100
10
1
0• different scenarios

Nakamura+2016

10

20
30
redshift z

40

high-z50

event rates for Pop III (standard), Pop I and II (OLD), and PBBH merger as. These rates are derived by diﬀerentiating the cumulative event rate in Fig. 5o ln z. Note here that the detectability may change by the mass distribution

Nakamura+2016; Koushiappas & Loeb 2017

Key observation: high-z events
Koushiappas & Loeb 2017

In addition, the assumption of afunctitrum of black holes is not realistic. A range
masses is most likely present. The e↵ect
assumption have been studied in the conte
ing the current rate of observed black hole mwith LIGO [48–55]. In our case, such a bla
function will alter the shape of N (z), but
zmax is negligible since the factors that gi
cuto↵ remain as discussed earlier (namely
the halo mass function and the decline inhigh redshifts).
The prediction of a maximum redshift fmerger events can be tested with future
wave detectors. In particular, Cosmic Exp
have the ability to detect events at these v
shifts. Given the current design capabilities
plorer will be able to detect the merger ofhole pairs at 10 significance out to redsh
and at 5 significance to redshift z ⇡ 44 [8limits are shown as vertical dashed lines inAny detection of an event rate greater tha
from a redshift greater than zmax ⇡ 40 wi
implications for cosmology. It would mea• different scenarios

predict different
event rates at z ≳15• accessible in 3rdgen. experiments

maximum z ~ 40
for astrophysical origin

FIG. 3: The number of gravitational wave events of mBH =30M black hole pairs originating from redshifts greater thanz (Equation 1) as a function of redshift. The blue curve corresponds to the upper limit on the halo mass function [30], a
low value of Mmin (i.e., ignoring the e↵ects of a relative speed

“High-z” events?

• from GW observations we do not directly
measure their redshifts• we measure luminosity distance, which isaffected by gravitational lensing• lensing magnification µ can bias redshiftinferred from the luminosity distance, andalso chirp mass

p
rp
or
or
#
#
n
on
le
le
of
of

9)
9)

ax
ax

correction of lensing magnification µ, as
mass’ Mobs , which is the chirp mass
mass’ Mobs , which is the chirp mass inwaveform, redshift
again without
the correctio
Observed
andmass
waveform, again without the correction
Theyaresimplydefinedaszobs defined• “observed
They areredshift
simply” defined
as as

(z)
D
L
(z)
D
L
(z
)
=
,
D
√
L
obs
DL (zobs ) = √ µ ,µ

μ: magnification factor• “observed chirp mass” Mobs defined as
+zz
11+
=
M.
M
obs =
M.
Mobs
+zzobsobs
11 +By differentiating
differentiatingequation
equation(25)(25)we
wecan
can
o
/dz
anddRdtion ofof thethe event
eventrate,
rate,dR
dRobsobs/dz
obsandobs

MO MNRAS 480(2018)3842

Distributions with lensing effects• redshift and mass dist. of binary BH mergers
taking full account of gravitational lensing• various scenarios: PopI/II, Pop-III, PBH• various experiments: aLIGO, KAGRA, ET,
CE, B-DECIGO• check how lensing (de-)magnification modify
these distributions

Strong lensing of BH mergers• difficult to identify multiple images given the poor
localization on the sky→ treat multiple images as distinct events• some images magnified and some demagnified
μ~6
μ~8
μ~0.3

μ~4
B1422+231

MO MNRAS 480(2018)3842

Magnification PDF• new hybrid

101

Pwl
Psl
total
z=10

100

dP/d ln µ

10−1
10−2

analytic model,
strong lens fromMonte Carlo

10−4
10−5
10−6
0.1

1

10

100

magnification µ

demagnified
100
10−1

weak+strong lens

• weak lens from

10−3

101

model combining

z=1
magnified
z=3
z=10
z=30

• long tails at highand low μMO MNRAS 480(2018)3842

Result: advanced LIGO
105

103
Pop-I/IIzobs distribution

3dRobs/dMobs [yr−1]

10

Pop-I/II

101

10−1

⟨µ⟩

10−3
0
3
10

10

Mobs distribution

1

10−1

w/ lensing

10−3

w/o lensing

0.2

0.4

0.6

0.8

1

10−5
0
3
10

102

102

101

101

⟨µ⟩

dRobs/dzobs [yr−1]

aLIGO

100

100

10−1
0

10−1
0

0.2

0.4

0.6

observed redshift zobs

0.8

1

20

40

60

80

100

20

40

60

80

100

observed chirp mass Mobs [M⊙]excess due tomagnified events(see also Dai+2017)

MO MNRAS 480(2018)3842

Result: Cosmic Explorer
105

107
Pop-I/II105

zobs distribution

103

w/ lensing

101
10−1

Pop-I/IIdRobs/dMobs [yr−1]

dRobs/dzobs [yr−1]

CE

w/o lensing
10

20

30

10−1
10−3
10−5
0
3
10

102

102

101

101

100

100

10−1
0

10−1
0

10

20

observed redshift zobs

30

Mobs distribution

101

⟨µ⟩

⟨µ⟩

10−3
0
3
10

103

excess due todemagnified events

20

40

60

80

100

120

20

40

60

80

100

120

observed chirp mass Mobs [M⊙]excess due tomagnified events(see also Dai+2017)

Effect of lensing (de-)magnification• produce apparently very high-z and very
high mass binary BH merger events• high-z events due to demagnification, andhigh mass events due to magnification• those events are strongly lensed, so shouldbe accompanied by other multiple images

MO MNRAS 480(2018)3842

Expected multiple image pairs

M. Oguri• advanced LIGO

1.0

strain [10 21]

strain [10 21]− time delay ≲1day− high, similar μ− Robs < 1 yr−1

0.5
0.0
0.5
1.0
0.25

Hanford

0.30

1.0
0.5
0.0

time

0.5
1.0

Hanford0.35 0.25 0.40 0.30 0.45 0.35

1.0

strain [10 21]

strain [10 21]

time [sec]

0.5
0.0
0.5
1.0

Livingston

0.40

0.45

time [sec]

≲1day

1.0
0.5
0.0
0.5
1.0

Livingston

3. Distributions of time delays and magnifications for pairs of multiple
imagesfromthe 0.40
mocklens catalogues.
As in Fig. 12, we
0.25
0.30
0.35 0.25
0.30strong
0.45 0.35
0.40
0.45

GravitationallylensedGW??
3852
M. Oguri
S190828l

S190828j

separatedby 21 min

21
min
(!)
Figure 13. Distributions of time delays and magnifications for pairs of multiple imdata of the Pop-I/II model from 3000 years and 1 year observations for advanced LIG

MO MNRAS 480(2018)3842

Expected multiple image pairs• Cosmic Explorer− time delay~10-100 days

1.0
strain [10 21]

0.5
0.0
0.5
1.0
0.25

1.0
0.5
0.0
1.0

Hanfordstrain [10 21]

0.30

0.35

0.40

0.45

0.30

0.35

1.0
0.5

0.40 0.0

1.0
0.5
0.0

ltiple images from the mock strong lens catalogues. As in Fig. 12, we plot mock0.45

~10-100 day

0.5
1.0

0.25

1.0

Hanfordtime [sec]time [sec]

0.5

time

0.5

0.25

strain [10 21]

strain [10 21]− different μ− Robs ~ O(103) yr−1

Livingston

0.30

0.35

time [sec]

0.40

0.45

MO MNRAS 480(2018)3842

Binary BH distribution: Summary• pronounced lensing effect at high zobs
and Mobs• the discovery of apparently very high-z events
does not necessarily support PBH scenario• predictions on multiple image pairs• see the paper for detailed results for different
BH merger scenarios and GW experiments

Conclusion• interesting synergies between GW andlarge-scale structure/gravitational lensing− spatial clustering of GW sources− observables affected by weak and strong
gravitational lensing• more work needed to fully exploit the potential
of GW observations!

Review article arXiv:1907.06830(covering SN, GRB, FRB, GW)
Strong gravitational lensing of explosive transients

0v1 [astro-ph.CO] 16 Jul 2019

Masamune Oguri1,2,3
1 Research Center for the Early Universe, University of Tokyo, Tokyo 113-0033,

Japan
2 Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
3 Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,
WPI), University of Tokyo, Chiba 277-8582, Japan
E-mail: masamune.oguri@ipmu.jp
Abstract. Recent rapid progress in time domain surveys makes it possible todetect various types of explosive transients in the Universe in large numbers,some of which will be gravitationally lensed into multiple images. Althougha large number of strongly lensed distant galaxies and quasars have alreadybeen discovered, strong lensing of explosive transients opens up new applications,
including improved measurements of cosmological parameters, powerful probesof small scale structure of the Universe, and new observational tests of dark
matter scenarios, thanks to their rapidly evolving light curves as well as theircompact sizes. In particular, the compactness of these transient events indicatesthat the wave optics e↵ect plays an important role in some cases, which can leadto totally new applications of these lensing events. Recently we have witnessed
first discoveries of strongly lensed supernovae, and strong lensing events of othertypes of explosive transients such as gamma-ray bursts, fast radio bursts, andgravitational waves from compact binary mergers are expected to be observed
soon. In this review article, we summarize the current state of research on strong
gravitational lensing of explosive transients and discuss future prospects.

Keywords: cosmology, gravitational lensing, transients