testing gr with gw polarizations - dcc-llo.ligo.org · max isi - amaldi 2017 3 ligo-g1701301 it is...

Testing GR with GW polarizations

Maximiliano Isi

LIGO Laboratory, California Institute of Technology

July 12, 2017 @ Amaldi12

LIGO-G1701301

using LIGO and Virgo

https://dcc.ligo.org/LIGO-G1701301

LIGO-G1701301Max Isi - Amaldi 2017 2

Testing GR with GWs

dispersion

agreement with NR

self-consistency

…

not about polarizations!there are currently no model-independent

measurements of GW polarizations

we have already learned a lot from transients:


it is important to probe GW polarizations

we can do so with current detectors

using long-lived signals

[tl;dr]

[too long ; didn’t read]


x

y

z

x

x

y

z

y

z

y

x

y

plus

cross

vector x

vector y

breathing

longitudinal

LIGO-G1701301Max Isi - Amaldi 2017

Theory + x x y b l

General Relativity

GR in noncompactified 4/6D Minkowski

Einstein-Æther

5D Kaluza-Klein

Randall-Sundrum braneworld

Dvali-Gabadadze-Porrati braneworld

Brans-Dicke

f(R) gravity

Bimetric theory

Four-Vector Gravity

allowed / depends / forbiddenNishizawa et al., Phys. Rev. D 79, 082002 (2009) [except G4v & Einstein-Æther].

5


motivation

GR makes unequivocal prediction that only + & x should propagate

polarizations are go/no-go test, so let’s check!


breathing

longitudinal

plus

cross

vector x

vector y

7


antenna pattern for cross polarization

8

detector

source

*


persistent signals

antenna patterns leave imprint in

persistent signals characteristic of

each polarization

continuous-wavesstochastic background


new bayesian analyses

detect long GWs of any polarization(from known pulsars, or a stochastic background)

distinguish between GR and non-GR

limit amplitude of scalar/vector modes

}model selection

➜ parameterestimation

Isi et al. (2017) [arXiv:1703.07530]

Callister et al. (2017) [arXiv:1704.08373]

http://arxiv.org/abs/1703.07530



CW[arXiv:1703.07530]

NASA / CXC / SAO

11

crab pulsar

one of ~200 known pulsars potentially in LIGO’s band

continuous waves

http://www.nasa.gov/

http://chandra.harvard.edu/

http://www.cfa.harvard.edu/sao/index.html


CW[arXiv:1703.07530]

12

�(t) ⇡ 2⇡ ⇥ (2frot

)+ doppler and other timing corrections

h(t) = h01

2

�1 + cos

2 ◆�F+(t) cos�(t) + h0 cos ◆ F⇥(t) sin�(t)

h0

, overall strength; ◆, inclination; F (t), antenna pattern; frot

, rotational frequency

simple form, in general relativity:

continuous wavescoherent, monochromatic, well-localized

in a generic metric theory of gravity:

p 2 {+, ⇥, x, y, s}

h(t) =X

p

Fp(t)ap cos(�(t) + �p)

polarization amplitude

phase offset


CW[arXiv:1703.07530]

tensor

vector scalar

polarization

antenna pattern

amplitude modulationover a sidereal day

Crab pulsar LIGO H1

13

time (h) time (h)

Crab pulsar LIGO H1

Crab pulsar LIGO H1

time (h)

ante

nn

a r

espon

se


CW[arXiv:1703.07530]signal vs noise

14

10�28 10�27 10�26 10�25

hGR

0

101

102

103

104

lnO

m N

Any

GR

tensor injections

odds(detection statistic)

Crab H1L1V1 1yr advanced design


CW[arXiv:1703.07530]

15

10�28 10�27 10�26 10�25

hG4V

0

101

102

103

104

lnO

m N

Any

GR

vector injections


vector


signal vs noise


CW[arXiv:1703.07530]

16

10�28 10�27 10�26 10�25

hGR

10�28

10�27

10�26

10�25

10�24h

b

0

101

103

105

lnBG

RN

scalar-tensor injections

scalaramplitude

signal

noise


gr signal vs noise


CW[arXiv:1703.07530]

17

10�28 10�27 10�26 10�25

hGR

10�28

10�27

10�26

10�25

10�24h

b

0

101

103

105

lnO

S N


scalaramplitude

Crab H1L1V1 1yr advanced design signal

noise

any signal vs noise


CW[arXiv:1703.07530]

18

10�28 10�27 10�26 10�25

hGR

10�28

10�27

10�26

10�25

10�24h

b

0

102

104

lnO

nG

RG

R


scalaramplitude

not GR

GR


non-gr vs gr


CW[arXiv:1703.07530]

19

102 103

fGW (Hz)

10�27

10�26

10�25

h95

%b

Results

ASD

102 103

10�24

10�23

pS

n(1

/pH

z)

scalar upper limits

sensitivity projections for

design aLIGO + Virgo

(each point represents one pulsar)


CW[arXiv:1703.07530]

20

vector upper limits

102 103

fGW (Hz)

10�27

10�26

10�25

h95

%v

Results

ASD

102 103 10�24

10�23

pS

n(1

/pH

z)

hv

⌘�h2

x

+ h2

y

�1/2

sensitivity projections for

design aLIGO + Virgo

(each point represents one pulsar)

SB


[arXiv:1704.08373]

21

stochastic backgroundincoherent superposition of myriad unresolvable sources

SNR (top) and 90%-confidence upper-limits (bottom) from radiometer stochastic background search

[Abbott et al., PRL 118, 121102 (2017)]

see Andrew Mata’s overview talk on Friday!

https://link.aps.org/doi/10.1103/PhysRevLett.118.121102

SB


[arXiv:1704.08373]

22

measure correlated strain power in two detectors

incoherent, broadband, all-sky

in a generic metric theory of gravity:

p 2 {+, ⇥, x, y, s}polarization amplitude

spectral index(“slope”)

stochastic background

with the canonical GW energy density usually parametrized by

⌦(f) = ⌦0 (f/f0)↵

overlap-reductionfunction

Dh̃⇤1(f)h̃

⇤2(f

0)E=

3H20

20⇡2�(f � f 0)|f |�3

X

p

⌦p0

✓f

f0

◆↵p

�p(f)

Dh̃⇤1(f)h̃

⇤2(f

0)E=

3H20

20⇡2�(f � f 0)|f |�3⌦(f)�(f)

SB


[arXiv:1704.08373]stochastic background

0 50 100 150 200 250 300 350 400

f (Hz)

�1.0

�0.8

�0.6

�0.4

�0.2

0.0

0.2

0.4

0.6

�(f

)

Hanford-Livingston

Tensor

Vector

Scalar

0 50 100 150 200 250 300 350 400

f (Hz)

�0.25

�0.20

�0.15

�0.10

�0.05

0.00

0.05

0.10

0.15

0.20

�(f

)

Livingston-Virgo

Tensor

Vector

Scalar

overlap reduction functions encode effect of time-of-flight and differences between polarizations

23

�(f) =5

8⇡

X

p

Z

skydn̂ ei2⇡fn̂·�~x/cF p

1 (n̂)Fp

2 (n̂)

sky location

detector separation

SB


[arXiv:1704.08373]

10�10 10�9 10�8

Tensor ⌦0

0

20

40

60

80

100ln

Osi

gn

signal vs noisetensor injections


24

(spec. index 2/3)

H1L1 3yr advanced design

SB


[arXiv:1704.08373]

10�10 10�9 10�8

Vector ⌦0

0

20

40

60

80

100ln

Osi

gn

signal vs noisevector injections


25

(spec. index 2/3)


SB


[arXiv:1704.08373]

10�10 10�9 10�8

Scalar ⌦0

0

20

40

60

80

100ln

Osi

gn

signal vs noisescalar injections


26


(spec. index 2/3)

SB


[arXiv:1704.08373]

�10.5 �10.0 �9.5 �9.0 �8.5 �8.0

Tensor log ⌦T0

�10.5

�10.0

�9.5

�9.0

�8.5

�8.0

�7.5Sca

lar

log

⌦S 0

�3

0

3

10

30

507090

lnO

sig

n


scalaramplitude

signal

noise

H1L1V1 3yr advanced design

27

(spec. index 2/3)

non-gr vs gr

SB


[arXiv:1704.08373]

�10.5 �10.0 �9.5 �9.0 �8.5 �8.0

Tensor log ⌦T0

�10.5

�10.0

�9.5

�9.0

�8.5

�8.0

�7.5Sca

lar

log

⌦S 0

�3

0

3

10

30

507090

lnO

ngr

gr

scalaramplitude

not GR

GR

H1L1V1 3yr advanced design

28

(spec. index 2/3)


non-gr vs gr

SB


[arXiv:1704.08373]

29

3yr sensitivity projections for design aLIGO + Virgo

�13�12�11�10�9 �8 �7 �6

log ⌦T0

log ⌦T0 = �11.71+1.02

�0.83

�13�12�11�10�9 �8 �7 �6

log ⌦V0

log ⌦V0 = �11.63+1.11

�0.90

�13�12�11�10�9 �8 �7 �6

log ⌦S0

log ⌦S0 = �11.69+1.02

�0.84

�8�6�4�2 0 2 4 6 8↵T

↵T = �0.40+2.49�2.50

�8�6�4�2 0 2 4 6 8↵V

↵V = 0.17+2.38�2.69

�8�6�4�2 0 2 4 6 8↵S

↵S = �0.37+2.48�2.55

tensor vector scalar

amplitudes


slopes

log⌦

S0 < �10.0log⌦

V0 < �9.9log⌦

T0 < �10.1

projected 95%-credible amplitude upper limits

gray histograms are LIGO-only results, dashed lines mark priors

parameter estimation

SB


[arXiv:1704.08373]

�13�12�11�10�9 �8 �7 �6

log ⌦T0

log ⌦T0 = �8.73+0.15

�0.22

�13�12�11�10�9 �8 �7 �6

log ⌦V0

log ⌦V0 = �11.22+1.46

�1.20

�13�12�11�10�9 �8 �7 �6

log ⌦S0

log ⌦S0 = �8.70+0.18

�0.33

�8�6�4�2 0 2 4 6 8↵T

↵T = 0.88+0.88�0.77

�8�6�4�2 0 2 4 6 8↵V

↵V = �0.26+2.03�2.53

�8�6�4�2 0 2 4 6 8↵S

↵S = 0.60+0.78�0.51


amplitudes


slopes

30

3yr scalar-tensor signal with design aLIGO + Virgo

gray histograms are LIGO-only results, dashed lines mark priors

Virgo does not increase sensitivity but helps

break degeneracy between scalar and vector

parameter estimation


we are now able to detect persistent signals of any

polarization content in a model-independent way

we can directly measure polarization content and

quantify agreement with GR

this will allow us to explore a new side of gravity!

conclusion

31

[arXiv:1703.07530] | [arXiv:1704.08373]

thank you!



testing gr with gw polarizations - dcc-llo.ligo.org · max isi - amaldi 2017 3 ligo-g1701301 it is...

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