Cosmography with
ground- and space-based
detectors
X LISA Symposium - Gainesville, Florida, May 19-23 2014
B.S. Sathyaprakash
School of Physics and Astronomy, Cardiff University
Friday, 23 May 2014
Outline
Cosmography with LISA
Difficulties and how we might mitigate some of them
Cosmography with ground-based detectors
Measuring host redshifts from GW observations
alone
Cosmography from a population of observed sources
Friday, 23 May 2014
2
Why are inspirals standard sirens?
Luminosity distance D can be inferred if one can�
measure:
the flux of radiation F and
absolute luminosity L
DL =
L
4πF
Schutz Nature1986
Flux of gravitational waves determined by amplitude of
gravitational waves measured by our detectors
Absolute luminosity can be inferred from the rate f˙ at
which the frequency of a source changes
Not unlike Cephied variables except that f˙ is completely determined
by general relativity
Therefore compact binaries are self-calibrating standard
sirens
Friday, 23 May 2014
3
4
Cosmography with LISA
Friday, 23 May 2014
Cosmography from a single source
Gravitational wave (GW) observations alone cannot
measure the source’s redshift
This is certainly true for binary black holes
For binary neutron stars it might be a different story
If it is possible to identify the host galaxy then
can measure the source’s redshift in addition to luminosity distance
An ideal tool for cosmography and synergy between EM and GW
astronomy
LISA can measure signals with a very high (amplitude)
signal-to-noise ratio (~1000-10,000)
Should be possible to distinguish between different cosmological
models with a high-SNR single event
Friday, 23 May 2014
5
6
eLISA, z=0.5
108
107
500
1000
1400
106
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1600
5
1200
800
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104
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Inset: ET SNRs
Inspiral signal
only
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Friday, 23 May 2014
106
107
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Sathyaprakash
and Schutz, LRR:
2014
7
Basic idea
Diagram:
Ned Wright: 2011
Red Shift z
2.3
1.6
0.8
0.0
0
2
4
6
8
10
Luminosity Distance in Gpc
Friday, 23 May 2014
7
Basic idea
Diagram:
Ned Wright: 2011
Red Shift z
2.3
1.6
⧱
0.8
0.0
0
2
4
6
8
10
Luminosity Distance in Gpc
Friday, 23 May 2014
7
Basic idea
Diagram:
Ned Wright: 2011
Red Shift z
2.3
1.6
⧱
0.8
⧱
0.0
0
2
4
6
8
10
Luminosity Distance in Gpc
Friday, 23 May 2014
7
Basic idea
Diagram:
Ned Wright: 2011
Red Shift z
2.3
1.6
⧱
⧱
0.8
⧱
0.0
0
2
4
6
8
10
Luminosity Distance in Gpc
Friday, 23 May 2014
We really only measure
But ...
8
The luminosity distance (redshifted comoving distance) and redshifted
masses
Mobs = (1 + z)Mintr , DL = (1 + z)D
Cannot measure the source’s redshift without EM identification
but this is difficult since GW detectors have poor sky localization
at least that is what we thought until recently
If we measure the source redshift we can deduce the intrinsic
mass of the source and resolve redshift-mass degeneracy
Distance measurement is corrupted by weak lensing
Holz and Hughes 2005; Van Den Broeck et al 2010
Correcting for or mitigating lensing would be important
Distance is strongly correlated with the unknown orbital
inclination of the source with respect to line-of-sight
Ajith and Bose 2009; Nissanke et al 2010
Friday, 23 May 2014
9
Localization Question:
Mitigated by Higher Signal Harmonics
Dominant radiation at twice the orbital frequency but
radiation is emitted at all multiples of the orbital frequency
Friday, 23 May 2014
Observed harmonics depend on the
inclination of the binary
10
Black:
Dominant
harmonic
Red:
Dominant
harmonic
Green:
Difference
All-Dominant
Friday, 23 May 2014
!"#$%&'()*+)%,#)-./012
Higher Signal Harmonics: Spectrum
3&'0 #%)12)4566718
Friday, 23 May 2014
11
Signal Harmonics and Sky Localization
12
Sky localization is improved by higher signal
harmonics that were neglected in earlier studies
Why does sky localization improve due to signal
harmonics?
Observed harmonics depend strongly on the inclination
of the binary
Inclination is strongly correlated with sky position
Harmonics help break distance-inclination and
inclination-sky position degeneracy
Friday, 23 May 2014
rovement
in terms
parameter
estimation when higher
order
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included.
higher
order
are included.
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Level of Improvement
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Friday, 23 May 2014
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Friday, 23 May 2014
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16
Addressing Weak Lensing
Correct for weak lensing by mapping the sky in the direction
of the source AND assume LISA will see many sources
Friday, 23 May 2014
(green) square-line curve. We consider our setup to be
Distance Measurement: Dominated by Lensing
17
0.06
0.05
!DL/DL
0.04
GW error
Weak lensing error #1
Weak lensing error #2
Combined error #1
Combined error #2
0.03
0.02
0.01
0
0
0.5
1
1.5
z
2
2.5
3
Lensing correction:
Simulation with a population
Fig.
2.—
Relative error in the luminosity
due to 2011
Shapiro
et al
2010
Petiteau,distance
Babak, Sesana:
weak lensing from (i) Shapiro et al. (2010) (circles) and from (ii)
Friday, 23 May 2014
18
Mitigating Lensing: Safety in Numbers
6
If LISA detects ~
30 events weak
lensing might
be mitigated
Use the original
Schutz idea of
not depending
on EM
identification
Friday, 23 May 2014
400
350
300
250
200
150
100
50
400
350
300
250
50
200
100
150
150
200
250
100
300
350
400 50
Petiteau,
Babak,
Sesana:in2011
Fig. 3.— Example
of error
box (cylinder)
part of the Mille
nium snapshot (cube with unit in Mpc). The blue cylinder is t
measurement error box and the green one also considers the pri
Posteriors on w: Two Different Realisations
0.08
0.02
0.06
0.015
0.01
0.08
0.008
0.06
0.04
0.02
0
-0.3 -0.15 0 0.15 0.3
0.006
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z = [0:1]
0.05
0.05
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z = [1:2]
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z = [2:3]
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0.02
0.02
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0.01
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-0.3 -0.15 0 0.15 0.3
w
0
-0.3 -0.15 0 0.15 0.3
w
0.004
0.005
0
-0.3 -0.15 0 0.15 0.3
w
0.002
0
-0.3 -0.15 0 0.15 0.3
w
Babak,
Sesana:
2011
Fig. 5.— Posterior distribution forPetiteau,
w for two
particular
realizaFriday,
23 May
2014 and bottom row). In each row, the left plot shows the
tions
(top
19
20
Cosmography with Ground-Based Detectors
Friday, 23 May 2014
Advanced LIGO Distance Reach to Binary
Coalescences
q=1
q=2
q=4
q=8
horizon distance (Mpc)
10
1.37
3
10
0.20
inspiral
only
redshift z
4
21
q is mass ratio
Buonanno and Sathyaprakash 2014
2
10
Friday, 23 May 2014
1
2
3
10
10
10
intrinsic total mass (solar mass)
0.02
Hubble Constant from Advanced Detectors
22
0.5
cos ι
AIGO or LIGO-Virgo-LCGT
network,
weneutron
expect 3/4
of
Assuming
short-hard-GRBs are
binary
stars
0.5
cos ι
this rate. If SHB collimation can be assumed, the rate
is further augmented by a factor of 1.12. At this rate,
we find that one year of observation should be enough
to measure H0 to an accuracy of ∼ 1% if SHBs are dominated by beamed NS-BH binaries using the “full” network of LIGO, Virgo, AIGO, and LCGT—admittedly,
cos(ι) optimistic scenario.
cos(ι) A general trend we
cos(ι)see is
our most
a network of five detectors (as opposed to our baseline
LIGO-Virgo network of three detectors) increases measurement accuracy in H0 by a factor of one and a half;
assuming that the SHB progenitor is a NS-BH binary
improves measurement accuracies by a factor of four or
greater. Errors in H0 are seen to improve by a factor of
at least two when we assume SHB collimation.
Aside from exploring the cosmological consequences of
these results, several other issues merit careful future
analysis.
Nissanke
et alOne
2009 general result we found is the importance
that prior distributions have on our final posterior PDF.
Friday, 23 May 2014
0.5
cos ι
1
1
1
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
0
0
0
+
100
200
DL (Mpc)
+
100
200
DL (Mpc)
100
200
DL (Mpc)
300
300
+
300
tectors. This allows us to make
Short gamma-ray bursts
Hubble Constant from Advanced Detectors
without EM counterparts
!
23
25 events:
!  H0= 69 ± 3 km s!1 Mpc!1 (~4% at 95% confidence)
!
50 events:
!  H0= 69 ± 2 km s!1 Mpc!1 (~3% at 95% confidence)
!
WMAP7+BAO+SnIa (Komatsu et al.,2011):
!  H0= 70.2 ± 1.4 km s!1 Mpc!1 (~2% at 68%
confidence)
!"#$"##%
Del Pozzo, 2011
Friday, 23 May 2014
&'()*+%,%-%./0&1%2(3*+41%56)7%#89#:%;8##%%
#<%
ET Distance Reach to Coalescing Binaries
Observed Mass
Intrinsic Mass
200
17.00
100
9.40
50
5.20
20
2.40
10
1.40
Redsh ift z
Lu m in osity distan ce !Gp c"
24
Sky!ave. dist . vs Obs. M, Ν#0.25, Χ#0
5
0.79
Sky!ave. dist . vs Ph ys. M, Ν#0.25, Χ#0
Sky!ave. dist . vs Obs. M, Ν#0.25, Χ#0.75
2
1
0.37
Sky!ave. dist . vs Ph ys. M, Ν#0.25, Χ#0.75
10
0
10
1
10
2
10
3
Total m ass !in M !"
Friday, 23 May 2014
10
4
0.20
Sathyaprakash et al 2012
ET Distance Reach to Coalescing Binaries
Observed Mass
Intrinsic Mass
200
17.00
100
9.40
50
5.20
Non-spinning
systems
20
2.40
10
1.40
Redsh ift z
Lu m in osity distan ce !Gp c"
24
Sky!ave. dist . vs Obs. M, Ν#0.25, Χ#0
5
0.79
Sky!ave. dist . vs Ph ys. M, Ν#0.25, Χ#0
Sky!ave. dist . vs Obs. M, Ν#0.25, Χ#0.75
2
1
0.37
Sky!ave. dist . vs Ph ys. M, Ν#0.25, Χ#0.75
10
0
10
1
10
2
10
3
Total m ass !in M !"
Friday, 23 May 2014
10
4
0.20
Sathyaprakash et al 2012
ET Distance Reach to Coalescing Binaries
Observed Mass
Intrinsic Mass
200
17.00
100
9.40
50
5.20
Non-spinning
systems
20
10
2.40
Spinning
systems
1.40
Redsh ift z
Lu m in osity distan ce !Gp c"
24
Sky!ave. dist . vs Obs. M, Ν#0.25, Χ#0
5
0.79
Sky!ave. dist . vs Ph ys. M, Ν#0.25, Χ#0
Sky!ave. dist . vs Obs. M, Ν#0.25, Χ#0.75
2
1
0.37
Sky!ave. dist . vs Ph ys. M, Ν#0.25, Χ#0.75
10
0
10
1
10
2
10
3
Total m ass !in M !"
Friday, 23 May 2014
10
4
0.20
Sathyaprakash et al 2012
10
ETB, z=1
3
25
10
20
Visibility
30
of Binary
in
50
70
M2 êMü
Inspirals
102
Einstein
60
80
10
Telescope
40
20
1
1
10
102
M1 êMü
Friday, 23 May 2014
103
ET: Measuring Dark Energy and Dark Matter
26
ET will observe 100’s of binary neutron stars and GRB
associations each year
GRBs could give the host location and red-shift, GW
observation provides DL
Class. Quantum Grav. 27 (2010) 215006
B S Sathyaprakash
al
Sathyaprakash
et al et2010
0.4
0.6
w
0.8
1
1.2
1.4
0.1
0
0.1
0.2
M
Friday, 23 May 2014
0.3
0.4
-state (EOS) of the dark energy component w dominates the evolu
27
Measuring
and its variation
with
ould be determined
by the w
observations.
In this paper,
wezshall ado
ft z:
Baskaran, Van Den Broeck, Zhao, Li, 2011
w(z) ≡ pde /ρde = w0 + wa z/(1 + z).
opted by many authors, including the DETF (dark energy task forc
ve w = w0 . However in the early Universe with z $ 1, the EOS b
nds to the present EOS, and wa describes the evolution of w(z).
rk energy is determined by the equation
ρ̇de + 3H(ρde + pde ) = 0,
dark energy in (3), we obtain that
ρde = ρde0 × E(z),
e of ρde at z = 0, and
E(z) ≡ (1 + z)3(1+w0 +wa ) e−3wa z/(1+z) .
Friday, 23 May 2014
28
GW cosmography without EM counterparts
Measure redshift from gravitational wave observations alone
Use a population of sources to statistically infer cosmological
parameters
Friday, 23 May 2014
[23] L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouve[37] incliR. A. Fisher
he sky
position
coordinates
ιso-called
and
ψL6+are
the orbital
[12]
F. M
Acernese
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mass
+
z)M
and
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liotou,
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Messenger-Read
Method:
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ationd[13]
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GW
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The
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(1
z)r.É.and
This
implies
that
itD,is49,not
possible
disentanqc/0703086
M.+Harry
the the
LIGO
Scientific
Classical
Make
post-Newtonian
Tidalto
Term
[24]LC. G.
and use
E. of
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S. Hild
ost-Newtonian
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glearXiv:gr-qc/9402014.
the
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the redshiftdomain
from the
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[25]
K.
Arun,
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(2010),
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1707
(1994).
+
α
x
(2) an
Ψ
(
f
)
=
2π
f
t
−
φ
−
been
determined
[17,
using
Newtonian
and
1PN
c“Einstein
k approxi[42] H. Müller
5/2
[27]
K.PP
G.
Arun, B. R.
Iyer,
B. 28]
S. cSathyaprakash,
and
P.
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Sun[16]
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et al.,
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(2005). (2011).
ceptualtodesign
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mations
the Rev.
tidal
The additional
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to
5/2
[43] http://ht
[28]
J. Vines,
E. E. B.
Flanagan,
andR.
T. N.
Hinderer,
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Rev.
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[17]
T.
Hinderer,
D.
Lackey,
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Phys.
a
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[44] K. Hotokeza
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where
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5 uchi, Phys. R
[29]
T. F.
Hinderer,
Astrophys.
J., 677,
1216
(2008),
arXiv:0711.2420.
�
�
�
[18]
Pannarale,
L.
Rezzolla,
F.
Ohme,
and
J.
S.
Read,
ArXiv
ea
a
5/2
2/3 �
a=1,2
3λ
24
11η
x
ph.HE].
[30]
A.
W.
Steiner,
J.
M.
Lattimer,
and
E.
F.
Brown,
Astrophys.
J.,
a
= (πM
f
)
and
the
corresponding
α
given
prints
(2011),
arXiv:1103.3526
[astro-ph.HE]. coefficients
tidal
k
N
Ψ722,
(E.f(2010),
)Flanagan
= arXiv:1005.0811
− [astro-ph.HE].
1Phys.
+ Rev. D, 77,
[45] C.(3)
K. Mishr
[19]
E. 33
and
T.
Hinderer,
021502
5
k/2
128η
χ
χ
M
a Phys.
aD, N
n [25].
Throughout
this
work
we
use
=
7
corresponding
[31] F. (2008).
Özel,
G. Baym,
and
T.
Güver,
Rev.
82,
101301
2
Phys.
Rev.
D
a=1,2
PP
c
c
k
5/2
a
�
a time
(2010),
arXiv:1002.3153
[astro-ph.HE].
o a[32]
3.5T.
PN
phase
expansion
(the
highest
known
at
the
7/2
�
�
k=0
a D, 80, 084035 (2009),
Damour and A. 5Nagar, Phys. Rev.
2
3 x
−The
3179 − 919χ
− 2286χ
260χ
aand
a +the
a
f publication).
parameters
t
φ
are
time
of5 coarXiv:0906.0096
[gr-qc].
c
c
28χ
M
a
[33] K. D. Kokkotas and G. Schafer, Mon. Not. R. Astron. Soc., 275,
lescence
and phase at coalescence and we use f to represent
301 (1995), arXiv:gr-qc/9502034.
2/3 the contributions from each NS5 (indexed
where
we
sum
over
Baiotti, T. Damour,
Giacomazzo,
and
2
he [34]
GWL. frequency
in theB. rest
frame A.ofNagar,
the
source.
that k
nsNote
5
Rezzolla,
Review λ
Letters,
261101
byL.a).
ThePhysical
parameter
= 105,
(2/3)R
k2(2010),
characterizes the
ns
the signal
is
modeled
using
the
point-particle
phase such
arXiv:1009.0521 [gr-qc].
the
iven
e acepa-tion
ntial
S
molTd to
racy
non.
-alid
ncy,
t
”] in
alone if the proper distance is unknown.
leading-order
effects
the quadrupole
tidal
phase.The
The
quantity Q(ϕ)
is a of
factor
that is determin
a neutron
star onofpost-Newtonian
the of
amplitude
response
the GW detectorbinary
and isdynam
a fun
been
determined
[17, 28]ϕusing
andθ 1PN
of the
nuisance
parameters
= (θ,Newtonian
φ, ι, ψ) where
and
to thecoordinates
tidal field. The
contr
the mations
sky position
and ιadditional
and ψ arephase
the orbital
a GW
from a BNSangles
systemrespectively.
is given by The sta
nation
andsignal
GW polarization
� frequency
�
�
post-Newtonian �
point-particle
domain
phase c
3λ
24
11η x
written
as
[25,
27]
Ψ (f) =
−
1+
128η χ
χ
M
�
π
3
�
5
+
α+ x260χ
Ψ ( f ) =−2π f t −3179
φ − − 919χ
−
2286χ
4 128ηx
28χ
where
the contributions
from eachpara
NS
where
we we
usesum
the over
post-Newtonian
dimensionless
a). f )Theand
parameter
λ = (2/3)R
k characte
x =by(πM
the corresponding
coefficients
α
strength
of the induced
quadrupole
an exte
in [25].
Throughout
this work
we use N given
= 7 correspo
strength of the induced quadrupole given an external tidal
Friday, 23 May 2014
30
Measurement
accuracy of
source redshift
1
APR
∆z/z
SLY
10−1 MS1
10−2
0.01
Messenger and Read, PRL, 2011
Friday, 23 May 2014
0.1
redshift z
1
Host redshifts from gravitational wave observations
31
Host-galaxy redshifts from gravitational-wave observations of binary neutron star mergers
C. Messenger,1 Kentaro Takami,2, 3 Sarah Gossan,4 Luciano Rezzolla,3, 2 and B. S. Sathyaprakash5
1
2
School of Physics and Astronomy,University of Glasgow, University Avenue, Glasgow, G12 8QQ, UK
Max-Planck-Institut für Gravitationsphysik, Albert Einstein Institut, Am Mühlenberg 1, 14476 Potsdam, Germany
3
Institut für Theoretische Physik, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany
4
TAPIR, California Institute of Technology, 1200 E California Blvd., Pasadena, CA 91125, USA
5
School of Physics and Astronomy, Cardiff University, 5, The Parade, Cardiff, UK, CF24 3AA
(Dated: Mon May 19 17:07:55 2014 +0200)
(commitID: 549ca0bc25679c083192dd8efb3b276f709733ed)
(LIGO-P1300211-v1)
Inspiralling compact binaries as standard sirens will become an invaluable tool for cosmology when we
enter the gravitational-wave detection era. However, a degeneracy in the information carried by gravitational
waves between the total rest-frame mass M and the redshift z of the source implies that neither can be directly
extracted from the signal, but only the combination M (1 + z), the redshifted mass. Recent work has shown
that for 3rd generation detectors, a tidal correction to the gravitational-wave phase in the late-inspiral signal of
binary neutron star systems could be used to break the mass-redshift degeneracy. We propose here to use the
signature encoded in the post-merger signal allowing the accurate extraction of the intrinsic rest-frame mass
of the source, in turn permitting the determination of source redshift and luminosity distance. The entirety of
this analysis method and any subsequent cosmological inference derived from it would be obtained solely from
gravitational-wave observations and hence be independent of the cosmological distance ladder. Using numerical
simulations of binary neutron star mergers of different mass, we model gravitational- wave signals at different
redshifts and use Bayesian parameter estimation to determine the accuracy with which the redshift and mass can
be extracted. We find that the Einstein Telescope can determine the source redshift to ∼ 10–20% at redshifts of
z < 0.04.
I. INTRODUCTION
to appear in PRX 2014
Friday, 23 May 2014
a network of detectors can determine the sky position, G
polarisation angle, orbital inclination and the distance to t
binary. The observed total mass, however, is not the system
Binary Neutron Star GW Spectrum - post Merger
M = 2.68268 M!
F2
F1
normalised power P
M = 2.75674 M!
M = 2.83252 M!
M = 2.91008 M!
M = 2.97806 M!
1.0
1.5
2.0
f (kHz)
Friday, 23 May 2014
2.5
3.0
3.5
32
Measurement Accuracies of Char. Frequencies
3.0
f (kHz)
2.5
2.0
1.5
1.0
f2
f1
2.70
2.80
M (M!)
Friday, 23 May 2014
2.90
3.00
33
How well can we measure z?
Friday, 23 May 2014
34
35
Hubble without the Hubble:
Cosmology using advanced gravitational-wave detectors alone
Stephen R. Taylor∗
Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, UK
Jonathan R. Gair†
Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, UK
Ilya Mandel‡
NSF Astronomy and Astrophysics Postdoctoral Fellow,
MIT Kavli Institute, Cambridge, MA 02139; and
School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT
(Dated: January 31, 2012)
We investigate a novel approach to measuring the Hubble constant using gravitational-wave (GW)
signals from compact binaries by exploiting the narrowness of the distribution of masses of the
underlying neutron-star population. Gravitational-wave observations with a network of detectors
will permit a direct, independent measurement of the distance to the source systems. If the redshift
of the source is known, these inspiraling double-neutron-star binary systems can be used as standard
Cosmology
the lights
off: Standard
sirens
the Einstein
Telescope
era
sirens
to extractwith
cosmological
information.
Unfortunately,
theinredshift
and the system
chirp mass
are degenerate in GW observations. Thus, most previous work has assumed that the source redshift
Stephen
R. Taylor∗ and
Jonathan
R. Gair† a novel method of using
is obtained from electromagnetic
counterparts.
However,
we investigate
Institute of
Astronomy,
Madingley
Road, Cambridge,
0HA, UK
these systems as standard
sirens
with GW
observations
alone. In CB3
this paper,
we explore what we
(Dated:
July
6,
2012)
can learn about the background cosmology and the mass distribution of neutron stars from the
set of neutron-star
(NS)
mergers
detected by
such a using
network.
We use a Bayesian
formalism to
We explore the
prospects
for constraining
cosmology
gravitational-wave
(GW) observations
neutron
binaries inspiral
by the proposed
Einstein
narrowness the
of the
analyze
catalogs
of NS-NS
detections.
WeTelescope
find that(ET),
it isexploiting
possible the
to constrain
Hubble
Friday,
23ofMay
2014 star
binary
system
mass could
conceivably
the
36
udies
due
to
the
divergence
at
high
redshift.
mple
ansatz
for
the
relationship
between
lying Cosmology
neutron star without
mass distribution.
The
chirp
mass
EM
Counterparts
The ET horizon
distance
for
a system
lying
oo-Sahni-Starobinsky
ansatz
[69]
models
the
distribution
parameters
and
the
underdistribution is modeled as normal,
star
distribution.
The
chirp
mass w = −1
distr
tion mass
as
a
“tanh”
form
that
ensures
Th
2
Distribution of Chirp
Mass
M
∼
N
(µ
,
σ
),
c
modeled
c ansatz premes
andaswnormal,
→ 0 at low z. This
are t
2
rossing
ofNthe
divide” at w = −1,
withM
mean
and
deviation
∼
(µc ,“phantom
σstandard
c ),
dista
nce
phantom
fluids
can not
be √
explained
by a
ars
in
the
binary
system
would
need
to
have
3/5
3/5
grea
standard
(13)
µc ≈deviation
2(0.25) µNS , σc ≈ 2(0.25) σNS , with
the distribution
mean
at the
coupled
scalar field
[68].
Themaximum
ansatz weconsidadopt
√
write
3/5
3/5
σNS∈, [0, 0.3]M
(13) # .
2(0.25)
, CPL
c ≈
here
µNS
∈σ[1.0,
1.5]M
, σNS
#
k) is µthe
ansatz
[68,
70]
NS
unit
Θ [2
w(a) = w0 + wa (1 − a),
"
!
z
.
(22)
w(z) = w0 + wa
1+z
The
z was adopted by the Dark Energy Task Force
Taylor, Gair 2012
merg
as several desirable features. It depends on
Friday, 23 May 2014
Measuring dark energy EoS and its
variation with redshift
1
0.5
wa
0
7
−0.5
−1
−1.5
−1.4
−1.2
−1
w
0
Friday, 23 May 2014
−0.8
−0.6
Taylor, Gair 2012
37
Conclusions
LISA observations alone could measure
cosmological parameters, but ...
A lot depends on the true event rate
Also, will it really be possible to correct for weak lensing
Measurement errors achieved in the end are not really
comparable to what can be done by other means
Ground-based detectors are in a good shape
for cosmography
A population of sources helps mitigate weak lensing
Statistical approaches work pretty well
Friday, 23 May 2014
38
Determining the Large Scale Structure
Friday, 23 May 2014
39