of 15
Tests of General Relativity with GW170817
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
F. Acernese,
3, 4
K. Ackley,
5
C. Adams,
6
T. Adams,
7
P. Addesso,
8
R. X. Adhikari,
1
V. B. Adya,
9, 10
C. Affeldt,
9, 10
B. Agarwal,
11
M. Agathos,
12
K. Agatsuma,
13
N. Aggarwal,
14
O. D. Aguiar,
15
L. Aiello,
16, 17
A. Ain,
18
P. Ajith,
19
B. Allen,
9, 20, 10
G. Allen,
11
A. Allocca,
21, 22
M. A. Aloy,
23
P. A. Altin,
24
A. Amato,
25
A. Ananyeva,
1
S. B. Anderson,
1
W. G. Anderson,
20
S. V. Angelova,
26
S. Antier,
27
S. Appert,
1
K. Arai,
1
M. C. Araya,
1
J. S. Areeda,
28
M. Arène,
29
N. Arnaud,
27, 30
K. G. Arun,
31
S. Ascenzi,
32, 33
G. Ashton,
5
M. Ast,
34
S. M. Aston,
6
P. Astone,
35
D. V. Atallah,
36
F. Aubin,
7
P. Aufmuth,
10
C. Aulbert,
9
K. AultONeal,
37
C. Austin,
2
A. Avila-Alvarez,
28
S. Babak,
38, 29
P. Bacon,
29
F. Badaracco,
16, 17
M. K. M. Bader,
13
S. Bae,
39
P. T. Baker,
40
F. Baldaccini,
41, 42
G. Ballardin,
30
S. W. Ballmer,
43
S. Banagiri,
44
J. C. Barayoga,
1
S. E. Barclay,
45
B. C. Barish,
1
D. Barker,
46
K. Barkett,
47
S. Barnum,
14
F. Barone,
3, 4
B. Barr,
45
L. Barsotti,
14
M. Barsuglia,
29
D. Barta,
48
J. Bartlett,
46
I. Bartos,
49
R. Bassiri,
50
A. Basti,
21, 22
J. C. Batch,
46
M. Bawaj,
51, 42
J. C. Bayley,
45
M. Bazzan,
52, 53
B. Bécsy,
54
C. Beer,
9
M. Bejger,
55
I. Belahcene,
27
A. S. Bell,
45
D. Beniwal,
56
M. Bensch,
9, 10
B. K. Berger,
1
G. Bergmann,
9, 10
S. Bernuzzi,
57, 58
J. J. Bero,
59
C. P. L. Berry,
60
D. Bersanetti,
61
A. Bertolini,
13
J. Betzwieser,
6
R. Bhandare,
62
I. A. Bilenko,
63
S. A. Bilgili,
40
G. Billingsley,
1
C. R. Billman,
49
J. Birch,
6
R. Birney,
26
O. Birnholtz,
59
S. Biscans,
1, 14
S. Biscoveanu,
5
A. Bisht,
9, 10
M. Bitossi,
30, 22
M. A. Bizouard,
27
J. K. Blackburn,
1
J. Blackman,
47
C. D. Blair,
6
D. G. Blair,
64
R. M. Blair,
46
S. Bloemen,
65
O. Bock,
9
N. Bode,
9, 10
M. Boer,
66
Y. Boetzel,
67
G. Bogaert,
66
A. Bohe,
38
F. Bondu,
68
E. Bonilla,
50
R. Bonnand,
7
P. Booker,
9, 10
B. A. Boom,
13
C. D. Booth,
36
R. Bork,
1
V. Boschi,
30
S. Bose,
69, 18
K. Bossie,
6
V. Bossilkov,
64
J. Bosveld,
64
Y. Bouffanais,
29
A. Bozzi,
30
C. Bradaschia,
22
P. R. Brady,
20
A. Bramley,
6
M. Branchesi,
16, 17
J. E. Brau,
70
T. Briant,
71
F. Brighenti,
72, 73
A. Brillet,
66
M. Brinkmann,
9, 10
V. Brisson,
27,
P. Brockill,
20
A. F. Brooks,
1
D. D. Brown,
56
S. Brunett,
1
C. C. Buchanan,
2
A. Buikema,
14
T. Bulik,
74
H. J. Bulten,
75, 13
A. Buonanno,
38, 76
D. Buskulic,
7
C. Buy,
29
R. L. Byer,
50
M. Cabero,
9
L. Cadonati,
77
G. Cagnoli,
25, 78
C. Cahillane,
1
J. Calderón Bustillo,
77
T. A. Callister,
1
E. Calloni,
79, 4
J. B. Camp,
80
M. Canepa,
81, 61
P. Canizares,
65
K. C. Cannon,
82
H. Cao,
56
J. Cao,
83
C. D. Capano,
9
E. Capocasa,
29
F. Carbognani,
30
S. Caride,
84
M. F. Carney,
85
G. Carullo,
21
J. Casanueva Diaz,
22
C. Casentini,
32, 33
S. Caudill,
13, 20
M. Cavaglià,
86
F. Cavalier,
27
R. Cavalieri,
30
G. Cella,
22
C. B. Cepeda,
1
P. Cerdá-Durán,
23
G. Cerretani,
21, 22
E. Cesarini,
87, 33
O. Chaibi,
66
S. J. Chamberlin,
88
M. Chan,
45
S. Chao,
89
P. Charlton,
90
E. Chase,
91
E. Chassande-Mottin,
29
D. Chatterjee,
20
K. Chatziioannou,
92
B. D. Cheeseboro,
40
H. Y. Chen,
93
X. Chen,
64
Y. Chen,
47
H.-P. Cheng,
49
H. Y. Chia,
49
A. Chincarini,
61
A. Chiummo,
30
T. Chmiel,
85
H. S. Cho,
94
M. Cho,
76
J. H. Chow,
24
N. Christensen,
95, 66
Q. Chu,
64
A. J. K. Chua,
47
S. Chua,
71
K. W. Chung,
96
S. Chung,
64
G. Ciani,
52, 53, 49
A. A. Ciobanu,
56
R. Ciolfi,
97, 98
F. Cipriano,
66
C. E. Cirelli,
50
A. Cirone,
81, 61
F. Clara,
46
J. A. Clark,
77
P. Clearwater,
99
F. Cleva,
66
C. Cocchieri,
86
E. Coccia,
16, 17
P.-F. Cohadon,
71
D. Cohen,
27
A. Colla,
100, 35
C. G. Collette,
101
C. Collins,
60
L. R. Cominsky,
102
M. Constancio Jr.,
15
L. Conti,
53
S. J. Cooper,
60
P. Corban,
6
T. R. Corbitt,
2
I. Cordero-Carrión,
103
K. R. Corley,
104
N. Cornish,
105
A. Corsi,
84
S. Cortese,
30
C. A. Costa,
15
R. Cotesta,
38
M. W. Coughlin,
1
S. B. Coughlin,
36, 91
J.-P. Coulon,
66
S. T. Countryman,
104
P. Couvares,
1
P. B. Covas,
106
E. E. Cowan,
77
D. M. Coward,
64
M. J. Cowart,
6
D. C. Coyne,
1
R. Coyne,
107
J. D. E. Creighton,
20
T. D. Creighton,
108
J. Cripe,
2
S. G. Crowder,
109
T. J. Cullen,
2
A. Cumming,
45
L. Cunningham,
45
E. Cuoco,
30
T. Dal Canton,
80
G. Dálya,
54
S. L. Danilishin,
10, 9
S. D’Antonio,
33
K. Danzmann,
9, 10
A. Dasgupta,
110
C. F. Da Silva Costa,
49
V. Dattilo,
30
I. Dave,
62
M. Davier,
27
D. Davis,
43
E. J. Daw,
111
B. Day,
77
D. DeBra,
50
M. Deenadayalan,
18
J. Degallaix,
25
M. De Laurentis,
79, 4
S. Deléglise,
71
W. Del Pozzo,
21, 22
N. Demos,
14
T. Denker,
9, 10
T. Dent,
9
R. De Pietri,
57, 58
J. Derby,
28
V. Dergachev,
9
R. De Rosa,
79, 4
C. De Rossi,
25, 30
R. DeSalvo,
112
O. de Varona,
9, 10
S. Dhurandhar,
18
M. C. Díaz,
108
T. Dietrich,
13
L. Di Fiore,
4
M. Di Giovanni,
113, 98
T. Di Girolamo,
79, 4
A. Di Lieto,
21, 22
B. Ding,
101
S. Di Pace,
100, 35
I. Di Palma,
100, 35
F. Di Renzo,
21, 22
A. Dmitriev,
60
Z. Doctor,
93
V. Dolique,
25
F. Donovan,
14
K. L. Dooley,
36, 86
S. Doravari,
9, 10
I. Dorrington,
36
M. Dovale Álvarez,
60
T. P. Downes,
20
M. Drago,
9, 16, 17
C. Dreissigacker,
9, 10
J. C. Driggers,
46
Z. Du,
83
P. Dupej,
45
S. E. Dwyer,
46
P. J. Easter,
5
T. B. Edo,
111
M. C. Edwards,
95
A. Effler,
6
H.-B. Eggenstein,
9, 10
P. Ehrens,
1
J. Eichholz,
1
S. S. Eikenberry,
49
M. Eisenmann,
7
R. A. Eisenstein,
14
R. C. Essick,
93
H. Estelles,
106
D. Estevez,
7
Z. B. Etienne,
40
T. Etzel,
1
M. Evans,
14
T. M. Evans,
6
V. Fafone,
32, 33, 16
H. Fair,
43
S. Fairhurst,
36
X. Fan,
83
S. Farinon,
61
B. Farr,
70
W. M. Farr,
60
E. J. Fauchon-Jones,
36
M. Favata,
114
M. Fays,
36
C. Fee,
85
H. Fehrmann,
9
J. Feicht,
1
M. M. Fejer,
50
F. Feng,
29
A. Fernandez-Galiana,
14
I. Ferrante,
21, 22
E. C. Ferreira,
15
F. Ferrini,
30
F. Fidecaro,
21, 22
I. Fiori,
30
D. Fiorucci,
29
M. Fishbach,
93
R. P. Fisher,
43
J. M. Fishner,
14
M. Fitz-Axen,
44
R. Flaminio,
7, 115
M. Fletcher,
45
arXiv:1811.00364v2 [gr-qc] 19 Nov 2018
2
H. Fong,
92
J. A. Font,
23, 116
P. W. F. Forsyth,
24
S. S. Forsyth,
77
J.-D. Fournier,
66
S. Frasca,
100, 35
F. Frasconi,
22
Z. Frei,
54
A. Freise,
60
R. Frey,
70
V. Frey,
27
P. Fritschel,
14
V. V. Frolov,
6
P. Fulda,
49
M. Fyffe,
6
H. A. Gabbard,
45
B. U. Gadre,
18
S. M. Gaebel,
60
J. R. Gair,
117
L. Gammaitoni,
41
M. R. Ganija,
56
S. G. Gaonkar,
18
A. Garcia,
28
C. García-Quirós,
106
F. Garufi,
79, 4
B. Gateley,
46
S. Gaudio,
37
G. Gaur,
118
V. Gayathri,
119
G. Gemme,
61
E. Genin,
30
A. Gennai,
22
D. George,
11
J. George,
62
L. Gergely,
120
V. Germain,
7
S. Ghonge,
77
Abhirup Ghosh,
19
Archisman Ghosh,
13
S. Ghosh,
20
B. Giacomazzo,
113, 98
J. A. Giaime,
2, 6
K. D. Giardina,
6
A. Giazotto,
22,
K. Gill,
37
G. Giordano,
3, 4
L. Glover,
112
E. Goetz,
46
R. Goetz,
49
B. Goncharov,
5
G. González,
2
J. M. Gonzalez Castro,
21, 22
A. Gopakumar,
121
M. L. Gorodetsky,
63
S. E. Gossan,
1
M. Gosselin,
30
R. Gouaty,
7
A. Grado,
122, 4
C. Graef,
45
M. Granata,
25
A. Grant,
45
S. Gras,
14
C. Gray,
46
G. Greco,
72, 73
A. C. Green,
60
R. Green,
36
E. M. Gretarsson,
37
P. Groot,
65
H. Grote,
36
S. Grunewald,
38
P. Gruning,
27
G. M. Guidi,
72, 73
H. K. Gulati,
110
X. Guo,
83
A. Gupta,
88
M. K. Gupta,
110
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
123
O. Halim,
17, 16
B. R. Hall,
69
E. D. Hall,
14
E. Z. Hamilton,
36
H. F. Hamilton,
124
G. Hammond,
45
M. Haney,
67
M. M. Hanke,
9, 10
J. Hanks,
46
C. Hanna,
88
M. D. Hannam,
36
O. A. Hannuksela,
96
J. Hanson,
6
T. Hardwick,
2
J. Harms,
16, 17
G. M. Harry,
125
I. W. Harry,
38
M. J. Hart,
45
C.-J. Haster,
92
K. Haughian,
45
J. Healy,
59
A. Heidmann,
71
M. C. Heintze,
6
H. Heitmann,
66
P. Hello,
27
G. Hemming,
30
M. Hendry,
45
I. S. Heng,
45
J. Hennig,
45
A. W. Heptonstall,
1
F. J. Hernandez,
5
M. Heurs,
9, 10
S. Hild,
45
T. Hinderer,
65
D. Hoak,
30
S. Hochheim,
9, 10
D. Hofman,
25
N. A. Holland,
24
K. Holt,
6
D. E. Holz,
93
P. Hopkins,
36
C. Horst,
20
J. Hough,
45
E. A. Houston,
45
E. J. Howell,
64
A. Hreibi,
66
E. A. Huerta,
11
D. Huet,
27
B. Hughey,
37
M. Hulko,
1
S. Husa,
106
S. H. Huttner,
45
T. Huynh-Dinh,
6
A. Iess,
32, 33
N. Indik,
9
C. Ingram,
56
R. Inta,
84
G. Intini,
100, 35
H. N. Isa,
45
J.-M. Isac,
71
M. Isi,
1
B. R. Iyer,
19
K. Izumi,
46
T. Jacqmin,
71
K. Jani,
77
P. Jaranowski,
126
D. S. Johnson,
11
W. W. Johnson,
2
D. I. Jones,
127
R. Jones,
45
R. J. G. Jonker,
13
L. Ju,
64
J. Junker,
9, 10
C. V. Kalaghatgi,
36
V. Kalogera,
91
B. Kamai,
1
S. Kandhasamy,
6
G. Kang,
39
J. B. Kanner,
1
S. J. Kapadia,
20
S. Karki,
70
K. S. Karvinen,
9, 10
M. Kasprzack,
2
M. Katolik,
11
S. Katsanevas,
30
E. Katsavounidis,
14
W. Katzman,
6
S. Kaufer,
9, 10
K. Kawabe,
46
N. V. Keerthana,
18
F. Kéfélian,
66
D. Keitel,
45
A. J. Kemball,
11
R. Kennedy,
111
J. S. Key,
128
F. Y. Khalili,
63
B. Khamesra,
77
H. Khan,
28
I. Khan,
16, 33
S. Khan,
9
Z. Khan,
110
E. A. Khazanov,
129
N. Kijbunchoo,
24
Chunglee Kim,
130
J. C. Kim,
131
K. Kim,
96
W. Kim,
56
W. S. Kim,
132
Y.-M. Kim,
133
E. J. King,
56
P. J. King,
46
M. Kinley-Hanlon,
125
R. Kirchhoff,
9, 10
J. S. Kissel,
46
L. Kleybolte,
34
S. Klimenko,
49
T. D. Knowles,
40
P. Koch,
9, 10
S. M. Koehlenbeck,
9, 10
S. Koley,
13
V. Kondrashov,
1
A. Kontos,
14
M. Korobko,
34
W. Z. Korth,
1
I. Kowalska,
74
D. B. Kozak,
1
C. Krämer,
9
V. Kringel,
9, 10
B. Krishnan,
9
A. Królak,
134, 135
G. Kuehn,
9, 10
P. Kumar,
136
R. Kumar,
110
S. Kumar,
19
L. Kuo,
89
A. Kutynia,
134
S. Kwang,
20
B. D. Lackey,
38
K. H. Lai,
96
M. Landry,
46
R. N. Lang,
137
J. Lange,
59
B. Lantz,
50
R. K. Lanza,
14
A. Lartaux-Vollard,
27
P. D. Lasky,
5
M. Laxen,
6
A. Lazzarini,
1
C. Lazzaro,
53
P. Leaci,
100, 35
S. Leavey,
9, 10
C. H. Lee,
94
H. K. Lee,
138
H. M. Lee,
130
H. W. Lee,
131
K. Lee,
45
J. Lehmann,
9, 10
A. Lenon,
40
M. Leonardi,
9, 10, 115
N. Leroy,
27
N. Letendre,
7
Y. Levin,
5
J. Li,
83
T. G. F. Li,
96
X. Li,
47
S. D. Linker,
112
T. B. Littenberg,
139
J. Liu,
64
X. Liu,
20
R. K. L. Lo,
96
N. A. Lockerbie,
26
L. T. London,
36
A. Longo,
140, 141
M. Lorenzini,
16, 17
V. Loriette,
142
M. Lormand,
6
G. Losurdo,
22
J. D. Lough,
9, 10
C. O. Lousto,
59
G. Lovelace,
28
H. Lück,
9, 10
D. Lumaca,
32, 33
A. P. Lundgren,
9
R. Lynch,
14
Y. Ma,
47
R. Macas,
36
S. Macfoy,
26
B. Machenschalk,
9
M. MacInnis,
14
D. M. Macleod,
36
I. Magaña Hernandez,
20
F. Magaña-Sandoval,
43
L. Magaña Zertuche,
86
R. M. Magee,
88
E. Majorana,
35
I. Maksimovic,
142
N. Man,
66
V. Mandic,
44
V. Mangano,
45
G. L. Mansell,
24
M. Manske,
20, 24
M. Mantovani,
30
F. Marchesoni,
51, 42
F. Marion,
7
S. Márka,
104
Z. Márka,
104
C. Markakis,
11
A. S. Markosyan,
50
A. Markowitz,
1
E. Maros,
1
A. Marquina,
103
S. Marsat,
38
F. Martelli,
72, 73
L. Martellini,
66
I. W. Martin,
45
R. M. Martin,
114
D. V. Martynov,
14
K. Mason,
14
E. Massera,
111
A. Masserot,
7
T. J. Massinger,
1
M. Masso-Reid,
45
S. Mastrogiovanni,
100, 35
A. Matas,
44
F. Matichard,
1, 14
L. Matone,
104
N. Mavalvala,
14
N. Mazumder,
69
J. J. McCann,
64
R. McCarthy,
46
D. E. McClelland,
24
S. McCormick,
6
L. McCuller,
14
S. C. McGuire,
143
J. McIver,
1
D. J. McManus,
24
T. McRae,
24
S. T. McWilliams,
40
D. Meacher,
88
G. D. Meadors,
5
M. Mehmet,
9, 10
J. Meidam,
13
E. Mejuto-Villa,
8
A. Melatos,
99
G. Mendell,
46
D. Mendoza-Gandara,
9, 10
R. A. Mercer,
20
L. Mereni,
25
E. L. Merilh,
46
M. Merzougui,
66
S. Meshkov,
1
C. Messenger,
45
C. Messick,
88
R. Metzdorff,
71
P. M. Meyers,
44
H. Miao,
60
C. Michel,
25
H. Middleton,
99
E. E. Mikhailov,
144
L. Milano,
79, 4
A. L. Miller,
49
A. Miller,
100, 35
B. B. Miller,
91
J. Miller,
14
M. Millhouse,
105
J. Mills,
36
M. C. Milovich-Goff,
112
O. Minazzoli,
66, 145
Y. Minenkov,
33
J. Ming,
9, 10
C. Mishra,
146
S. Mitra,
18
V. P. Mitrofanov,
63
G. Mitselmakher,
49
R. Mittleman,
14
D. Moffa,
85
K. Mogushi,
86
M. Mohan,
30
S. R. P. Mohapatra,
14
M. Montani,
72, 73
C. J. Moore,
12
D. Moraru,
46
G. Moreno,
46
S. Morisaki,
82
B. Mours,
7
C. M. Mow-Lowry,
60
G. Mueller,
49
A. W. Muir,
36
3
Arunava Mukherjee,
9, 10
D. Mukherjee,
20
S. Mukherjee,
108
N. Mukund,
18
A. Mullavey,
6
J. Munch,
56
E. A. Muñiz,
43
M. Muratore,
37
P. G. Murray,
45
A. Nagar,
87, 147, 148
K. Napier,
77
I. Nardecchia,
32, 33
L. Naticchioni,
100, 35
R. K. Nayak,
149
J. Neilson,
112
G. Nelemans,
65, 13
T. J. N. Nelson,
6
M. Nery,
9, 10
A. Neunzert,
123
L. Nevin,
1
J. M. Newport,
125
K. Y. Ng,
14
S. Ng,
56
P. Nguyen,
70
T. T. Nguyen,
24
D. Nichols,
65
A. B. Nielsen,
9
S. Nissanke,
65, 13
A. Nitz,
9
F. Nocera,
30
D. Nolting,
6
C. North,
36
L. K. Nuttall,
36
M. Obergaulinger,
23
J. Oberling,
46
B. D. O’Brien,
49
G. D. O’Dea,
112
G. H. Ogin,
150
J. J. Oh,
132
S. H. Oh,
132
F. Ohme,
9
H. Ohta,
82
M. A. Okada,
15
M. Oliver,
106
P. Oppermann,
9, 10
Richard J. Oram,
6
B. O’Reilly,
6
R. Ormiston,
44
L. F. Ortega,
49
R. O’Shaughnessy,
59
S. Ossokine,
38
D. J. Ottaway,
56
H. Overmier,
6
B. J. Owen,
84
A. E. Pace,
88
G. Pagano,
21, 22
J. Page,
139
M. A. Page,
64
A. Pai,
119
S. A. Pai,
62
J. R. Palamos,
70
O. Palashov,
129
C. Palomba,
35
A. Pal-Singh,
34
Howard Pan,
89
Huang-Wei Pan,
89
B. Pang,
47
P. T. H. Pang,
96
C. Pankow,
91
F. Pannarale,
36
B. C. Pant,
62
F. Paoletti,
22
A. Paoli,
30
M. A. Papa,
9, 20, 10
A. Parida,
18
W. Parker,
6
D. Pascucci,
45
A. Pasqualetti,
30
R. Passaquieti,
21, 22
D. Passuello,
22
M. Patil,
135
B. Patricelli,
151, 22
B. L. Pearlstone,
45
C. Pedersen,
36
M. Pedraza,
1
R. Pedurand,
25, 152
L. Pekowsky,
43
A. Pele,
6
S. Penn,
153
C. J. Perez,
46
A. Perreca,
113, 98
L. M. Perri,
91
H. P. Pfeiffer,
92, 38
M. Phelps,
45
K. S. Phukon,
18
O. J. Piccinni,
100, 35
M. Pichot,
66
F. Piergiovanni,
72, 73
V. Pierro,
8
G. Pillant,
30
L. Pinard,
25
I. M. Pinto,
8
M. Pirello,
46
M. Pitkin,
45
R. Poggiani,
21, 22
P. Popolizio,
30
E. K. Porter,
29
L. Possenti,
154, 73
A. Post,
9
J. Powell,
155
J. Prasad,
18
J. W. W. Pratt,
37
G. Pratten,
106
V. Predoi,
36
T. Prestegard,
20
M. Principe,
8
S. Privitera,
38
G. A. Prodi,
113, 98
L. G. Prokhorov,
63
O. Puncken,
9, 10
M. Punturo,
42
P. Puppo,
35
M. Pürrer,
38
H. Qi,
20
V. Quetschke,
108
E. A. Quintero,
1
R. Quitzow-James,
70
F. J. Raab,
46
D. S. Rabeling,
24
H. Radkins,
46
P. Raffai,
54
S. Raja,
62
C. Rajan,
62
B. Rajbhandari,
84
M. Rakhmanov,
108
K. E. Ramirez,
108
A. Ramos-Buades,
106
Javed Rana,
18
P. Rapagnani,
100, 35
V. Raymond,
36
M. Razzano,
21, 22
J. Read,
28
T. Regimbau,
66, 7
L. Rei,
61
S. Reid,
26
D. H. Reitze,
1, 49
W. Ren,
11
F. Ricci,
100, 35
P. M. Ricker,
11
G. M. Riemenschneider,
147, 156
K. Riles,
123
M. Rizzo,
59
N. A. Robertson,
1, 45
R. Robie,
45
F. Robinet,
27
T. Robson,
105
A. Rocchi,
33
L. Rolland,
7
J. G. Rollins,
1
V. J. Roma,
70
R. Romano,
3, 4
C. L. Romel,
46
J. H. Romie,
6
D. Rosińska,
157, 55
M. P. Ross,
158
S. Rowan,
45
A. Rüdiger,
9, 10
P. Ruggi,
30
G. Rutins,
159
K. Ryan,
46
S. Sachdev,
1
T. Sadecki,
46
M. Sakellariadou,
160
L. Salconi,
30
M. Saleem,
119
F. Salemi,
9
A. Samajdar,
149, 13
L. Sammut,
5
L. M. Sampson,
91
E. J. Sanchez,
1
L. E. Sanchez,
1
N. Sanchis-Gual,
23
V. Sandberg,
46
J. R. Sanders,
43
N. Sarin,
5
B. Sassolas,
25
B. S. Sathyaprakash,
88, 36
P. R. Saulson,
43
O. Sauter,
123
R. L. Savage,
46
A. Sawadsky,
34
P. Schale,
70
M. Scheel,
47
J. Scheuer,
91
P. Schmidt,
65
R. Schnabel,
34
R. M. S. Schofield,
70
A. Schönbeck,
34
E. Schreiber,
9, 10
D. Schuette,
9, 10
B. W. Schulte,
9, 10
B. F. Schutz,
36, 9
S. G. Schwalbe,
37
J. Scott,
45
S. M. Scott,
24
E. Seidel,
11
D. Sellers,
6
A. S. Sengupta,
161
N. Sennett,
38
D. Sentenac,
30
V. Sequino,
32, 33, 16
A. Sergeev,
129
Y. Setyawati,
9
D. A. Shaddock,
24
T. J. Shaffer,
46
A. A. Shah,
139
M. S. Shahriar,
91
M. B. Shaner,
112
L. Shao,
38
B. Shapiro,
50
P. Shawhan,
76
H. Shen,
11
D. H. Shoemaker,
14
D. M. Shoemaker,
77
K. Siellez,
77
X. Siemens,
20
M. Sieniawska,
55
D. Sigg,
46
A. D. Silva,
15
L. P. Singer,
80
A. Singh,
9, 10
A. Singhal,
16, 35
A. M. Sintes,
106
B. J. J. Slagmolen,
24
T. J. Slaven-Blair,
64
B. Smith,
6
J. R. Smith,
28
R. J. E. Smith,
5
S. Somala,
162
E. J. Son,
132
B. Sorazu,
45
F. Sorrentino,
61
T. Souradeep,
18
A. P. Spencer,
45
A. K. Srivastava,
110
K. Staats,
37
D. A. Steer,
29
M. Steinke,
9, 10
J. Steinlechner,
34, 45
S. Steinlechner,
34
D. Steinmeyer,
9, 10
B. Steltner,
9, 10
S. P. Stevenson,
155
D. Stocks,
50
R. Stone,
108
D. J. Stops,
60
K. A. Strain,
45
G. Stratta,
72, 73
S. E. Strigin,
63
A. Strunk,
46
R. Sturani,
163
A. L. Stuver,
164
T. Z. Summerscales,
165
L. Sun,
99
S. Sunil,
110
J. Suresh,
18
P. J. Sutton,
36
B. L. Swinkels,
13
M. J. Szczepańczyk,
37
M. Tacca,
13
S. C. Tait,
45
C. Talbot,
5
D. Talukder,
70
N. Tamanini,
38
D. B. Tanner,
49
M. Tápai,
120
A. Taracchini,
38
J. D. Tasson,
95
J. A. Taylor,
139
R. Taylor,
1
S. V. Tewari,
153
T. Theeg,
9, 10
F. Thies,
9, 10
E. G. Thomas,
60
M. Thomas,
6
P. Thomas,
46
K. A. Thorne,
6
E. Thrane,
5
S. Tiwari,
16, 98
V. Tiwari,
36
K. V. Tokmakov,
26
K. Toland,
45
M. Tonelli,
21, 22
Z. Tornasi,
45
A. Torres-Forné,
23
C. I. Torrie,
1
D. Töyrä,
60
F. Travasso,
30, 42
G. Traylor,
6
J. Trinastic,
49
M. C. Tringali,
113, 98
L. Trozzo,
166, 22
K. W. Tsang,
13
M. Tse,
14
R. Tso,
47
L. Tsukada,
82
D. Tsuna,
82
D. Tuyenbayev,
108
K. Ueno,
20
D. Ugolini,
167
A. L. Urban,
1
S. A. Usman,
36
H. Vahlbruch,
9, 10
G. Vajente,
1
G. Valdes,
2
N. van Bakel,
13
M. van Beuzekom,
13
J. F. J. van den Brand,
75, 13
C. Van Den Broeck,
13, 168
D. C. Vander-Hyde,
43
L. van der Schaaf,
13
J. V. van Heijningen,
13
A. A. van Veggel,
45
M. Vardaro,
52, 53
V. Varma,
47
S. Vass,
1
M. Vasúth,
48
A. Vecchio,
60
G. Vedovato,
53
J. Veitch,
45
P. J. Veitch,
56
K. Venkateswara,
158
G. Venugopalan,
1
D. Verkindt,
7
F. Vetrano,
72, 73
A. Viceré,
72, 73
A. D. Viets,
20
S. Vinciguerra,
60
D. J. Vine,
159
J.-Y. Vinet,
66
S. Vitale,
14
T. Vo,
43
H. Vocca,
41, 42
C. Vorvick,
46
S. P. Vyatchanin,
63
A. R. Wade,
1
L. E. Wade,
85
M. Wade,
85
R. Walet,
13
M. Walker,
28
L. Wallace,
1
S. Walsh,
20, 9
G. Wang,
16, 22
H. Wang,
60
J. Z. Wang,
123
W. H. Wang,
108
Y. F. Wang,
96
R. L. Ward,
24
J. Warner,
46
M. Was,
7
J. Watchi,
101
B. Weaver,
46
L.-W. Wei,
9, 10
4
M. Weinert,
9, 10
A. J. Weinstein,
1
R. Weiss,
14
F. Wellmann,
9, 10
L. Wen,
64
E. K. Wessel,
11
P. Weßels,
9, 10
J. Westerweck,
9
K. Wette,
24
J. T. Whelan,
59
B. F. Whiting,
49
C. Whittle,
14
D. Wilken,
9, 10
D. Williams,
45
R. D. Williams,
1
A. R. Williamson,
59, 65
J. L. Willis,
1, 124
B. Willke,
9, 10
M. H. Wimmer,
9, 10
W. Winkler,
9, 10
C. C. Wipf,
1
H. Wittel,
9, 10
G. Woan,
45
J. Woehler,
9, 10
J. K. Wofford,
59
W. K. Wong,
96
J. Worden,
46
J. L. Wright,
45
D. S. Wu,
9, 10
D. M. Wysocki,
59
S. Xiao,
1
W. Yam,
14
H. Yamamoto,
1
C. C. Yancey,
76
L. Yang,
169
M. J. Yap,
24
M. Yazback,
49
Hang Yu,
14
Haocun Yu,
14
M. Yvert,
7
A. Zadrożny,
134
M. Zanolin,
37
T. Zelenova,
30
J.-P. Zendri,
53
M. Zevin,
91
J. Zhang,
64
L. Zhang,
1
M. Zhang,
144
T. Zhang,
45
Y.-H. Zhang,
9, 10
C. Zhao,
64
M. Zhou,
91
Z. Zhou,
91
S. J. Zhu,
9, 10
X. J. Zhu,
5
A. B. Zimmerman,
170, 92
M. E. Zucker,
1, 14
and J. Zweizig
1
(The LIGO Scientific Collaboration and the Virgo Collaboration)
1
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2
Louisiana State University, Baton Rouge, LA 70803, USA
3
Università di Salerno, Fisciano, I-84084 Salerno, Italy
4
INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
5
OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia
6
LIGO Livingston Observatory, Livingston, LA 70754, USA
7
Laboratoire d’Annecy de Physique des Particules (LAPP), Univ. Grenoble Alpes,
Université Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France
8
University of Sannio at Benevento, I-82100 Benevento,
Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
9
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany
10
Leibniz Universität Hannover, D-30167 Hannover, Germany
11
NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
12
University of Cambridge, Cambridge CB2 1TN, United Kingdom
13
Nikhef, Science Park 105, 1098 XG Amsterdam, The Netherlands
14
LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
15
Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil
16
Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy
17
INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy
18
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
19
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
20
University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
21
Università di Pisa, I-56127 Pisa, Italy
22
INFN, Sezione di Pisa, I-56127 Pisa, Italy
23
Departamento de Astronomía y Astrofísica, Universitat de València, E-46100 Burjassot, València, Spain
24
OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia
25
Laboratoire des Matériaux Avancés (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France
26
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
27
LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, F-91898 Orsay, France
28
California State University Fullerton, Fullerton, CA 92831, USA
29
APC, AstroParticule et Cosmologie, Université Paris Diderot,
CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,
Sorbonne Paris Cité, F-75205 Paris Cedex 13, France
30
European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
31
Chennai Mathematical Institute, Chennai 603103, India
32
Università di Roma Tor Vergata, I-00133 Roma, Italy
33
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
34
Universität Hamburg, D-22761 Hamburg, Germany
35
INFN, Sezione di Roma, I-00185 Roma, Italy
36
Cardiff University, Cardiff CF24 3AA, United Kingdom
37
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
38
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany
39
Korea Institute of Science and Technology Information, Daejeon 34141, Korea
40
West Virginia University, Morgantown, WV 26506, USA
41
Università di Perugia, I-06123 Perugia, Italy
42
INFN, Sezione di Perugia, I-06123 Perugia, Italy
43
Syracuse University, Syracuse, NY 13244, USA
44
University of Minnesota, Minneapolis, MN 55455, USA
45
SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
46
LIGO Hanford Observatory, Richland, WA 99352, USA
47
Caltech CaRT, Pasadena, CA 91125, USA
48
Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary
5
49
University of Florida, Gainesville, FL 32611, USA
50
Stanford University, Stanford, CA 94305, USA
51
Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
52
Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
53
INFN, Sezione di Padova, I-35131 Padova, Italy
54
MTA-ELTE Astrophysics Research Group, Institute of Physics, Eötvös University, Budapest 1117, Hungary
55
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland
56
OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia
57
Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
58
INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy
59
Rochester Institute of Technology, Rochester, NY 14623, USA
60
University of Birmingham, Birmingham B15 2TT, United Kingdom
61
INFN, Sezione di Genova, I-16146 Genova, Italy
62
RRCAT, Indore, Madhya Pradesh 452013, India
63
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
64
OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia
65
Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
66
Artemis, Université Côte d’Azur, Observatoire Côte d’Azur,
CNRS, CS 34229, F-06304 Nice Cedex 4, France
67
Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
68
Univ Rennes, CNRS, Institut FOTON - UMR6082, F-3500 Rennes, France
69
Washington State University, Pullman, WA 99164, USA
70
University of Oregon, Eugene, OR 97403, USA
71
Laboratoire Kastler Brossel, Sorbonne Université, CNRS,
ENS-Université PSL, Collège de France, F-75005 Paris, France
72
Università degli Studi di Urbino ’Carlo Bo,’ I-61029 Urbino, Italy
73
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
74
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
75
VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
76
University of Maryland, College Park, MD 20742, USA
77
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
78
Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France
79
Università di Napoli ’Federico II,’ Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
80
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
81
Dipartimento di Fisica, Università degli Studi di Genova, I-16146 Genova, Italy
82
RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.
83
Tsinghua University, Beijing 100084, China
84
Texas Tech University, Lubbock, TX 79409, USA
85
Kenyon College, Gambier, OH 43022, USA
86
The University of Mississippi, University, MS 38677, USA
87
Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”,
I-00184 Roma, Italyrico Fermi, I-00184 Roma, Italy
88
The Pennsylvania State University, University Park, PA 16802, USA
89
National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
90
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
91
Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA),
Northwestern University, Evanston, IL 60208, USA
92
Canadian Institute for Theoretical Astrophysics,
University of Toronto, Toronto, Ontario M5S 3H8, Canada
93
University of Chicago, Chicago, IL 60637, USA
94
Pusan National University, Busan 46241, Korea
95
Carleton College, Northfield, MN 55057, USA
96
The Chinese University of Hong Kong, Shatin, NT, Hong Kong
97
INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy
98
INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
99
OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia
100
Università di Roma ’La Sapienza,’ I-00185 Roma, Italy
101
Université Libre de Bruxelles, Brussels 1050, Belgium
102
Sonoma State University, Rohnert Park, CA 94928, USA
103
Departamento de Matemáticas, Universitat de València, E-46100 Burjassot, València, Spain
104
Columbia University, New York, NY 10027, USA
105
Montana State University, Bozeman, MT 59717, USA
106
Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
6
107
University of Rhode Island
108
The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
109
Bellevue College, Bellevue, WA 98007, USA
110
Institute for Plasma Research, Bhat, Gandhinagar 382428, India
111
The University of Sheffield, Sheffield S10 2TN, United Kingdom
112
California State University, Los Angeles, 5151 State University Dr, Los Angeles, CA 90032, USA
113
Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
114
Montclair State University, Montclair, NJ 07043, USA
115
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
116
Observatori Astronòmic, Universitat de València, E-46980 Paterna, València, Spain
117
School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
118
University and Institute of Advanced Research,
Koba Institutional Area, Gandhinagar Gujarat 382007, India
119
Indian Institute of Technology Bombay
120
University of Szeged, Dóm tér 9, Szeged 6720, Hungary
121
Tata Institute of Fundamental Research, Mumbai 400005, India
122
INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy
123
University of Michigan, Ann Arbor, MI 48109, USA
124
Abilene Christian University, Abilene, TX 79699, USA
125
American University, Washington, D.C. 20016, USA
126
University of Białystok, 15-424 Białystok, Poland
127
University of Southampton, Southampton SO17 1BJ, United Kingdom
128
University of Washington Bothell, 18115 Campus Way NE, Bothell, WA 98011, USA
129
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
130
Korea Astronomy and Space Science Institute, Daejeon 34055, Korea
131
Inje University Gimhae, South Gyeongsang 50834, Korea
132
National Institute for Mathematical Sciences, Daejeon 34047, Korea
133
Ulsan National Institute of Science and Technology
134
NCBJ, 05-400 Świerk-Otwock, Poland
135
Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland
136
Cornell Universtiy
137
Hillsdale College, Hillsdale, MI 49242, USA
138
Hanyang University, Seoul 04763, Korea
139
NASA Marshall Space Flight Center, Huntsville, AL 35811, USA
140
Dipartimento di Fisica, Università degli Studi Roma Tre, I-00154 Roma, Italy
141
INFN, Sezione di Roma Tre, I-00154 Roma, Italy
142
ESPCI, CNRS, F-75005 Paris, France
143
Southern University and A&M College, Baton Rouge, LA 70813, USA
144
College of William and Mary, Williamsburg, VA 23187, USA
145
Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco
146
Indian Institute of Technology Madras, Chennai 600036, India
147
INFN Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy
148
Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France
149
IISER-Kolkata, Mohanpur, West Bengal 741252, India
150
Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA
151
Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
152
Université de Lyon, F-69361 Lyon, France
153
Hobart and William Smith Colleges, Geneva, NY 14456, USA
154
Università degli Studi di Firenze, I-50121 Firenze, Italy
155
OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia
156
Dipartimento di Fisica, Università degli Studi di Torino, I-10125 Torino, Italy
157
Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland
158
University of Washington, Seattle, WA 98195, USA
159
SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
160
King’s College London, University of London, London WC2R 2LS, United Kingdom
161
Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
162
Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India
163
International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil
164
Villanova University, 800 Lancaster Ave, Villanova, PA 19085, USA
165
Andrews University, Berrien Springs, MI 49104, USA
166
Università di Siena, I-53100 Siena, Italy
167
Trinity University, San Antonio, TX 78212, USA
168
Van Swinderen Institute for Particle Physics and Gravity,
University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
7
169
Colorado State University, Fort Collins, CO 80523, USA
170
Department of Physics, University of Texas, Austin, TX 78712, USA
(Dated: November 20, 2018)
The recent discovery by Advanced LIGO and Advanced Virgo of a gravitational wave signal from
a binary neutron star inspiral has enabled tests of general relativity (GR) with this new type of
source. This source, for the first time, permits tests of strong-field dynamics of compact binaries
in presence of matter. In this paper, we place constraints on the dipole radiation and possible
deviations from GR in the post-Newtonian coefficients that govern the inspiral regime. Bounds on
modified dispersion of gravitational waves are obtained; in combination with information from the
observed electromagnetic counterpart we can also constrain effects due to large extra dimensions.
Finally, the polarization content of the gravitational wave signal is studied. The results of all tests
performed here show good agreement with GR.
INTRODUCTION
On August 17, 2017 at 12:41:04 UTC, the Advanced
LIGO and Advanced Virgo gravitational-wave (GW) de-
tectors made their first observation of a binary neutron
star inspiral signal, called GW170817 [1]. Associated
with this event, a gamma ray burst [2] was independently
observed, and an optical counterpart was later discovered
[3]. In terms of fundamental physics, these coincident
observations led to a stringent constraint on the differ-
ence between the speed of gravity and the speed of light;
allowed new bounds to be placed on local Lorentz invari-
ance violations; and enabled a new test of the equiva-
lence principle by constraining the Shapiro delay between
gravitational and electromagnetic radiation [2]. These
bounds, in turn, helped to strongly constrain the allowed
parameter space of alternative theories of gravity that
offered gravitational explanations for the origin of dark
energy [4–10] or dark matter [11].
In this paper we present a range of tests of general rela-
tivity (GR) that have not yet been done with GW170817.
Some of these are extensions of tests performed with
previously discovered binary black hole coalescences [12–
18], an important difference being that the neutron stars’
tidal deformabilities need to be taken into account in the
waveform models. The parameter estimation settings for
this analysis broadly match with those of [19, 20] which
reported the properties of the source GW170817.
Three types of tests are presented. In Sec. II, we study
the general-relativistic dynamics of the source, in partic-
ular constraining dipole radiation in the strong-field and
radiative regime and checking for possible deviations in
the post-Newtonian (PN) description of binary inspiral
by studying the phase evolution of the signal. Sec. III
focuses on the way gravitational waves propagate over
large distances. Here we look for anomalous dispersion,
which enables complementary bounds on violations of lo-
cal Lorentz invariance to those of [2]; constraints on large
extra spatial dimensions are obtained by comparing the
distance inferred from the GW signal with the one in-
ferred from the electromagnetic counterpart. Finally, in
Sec. IV constraints are placed on alternative polarization
states, where this time the position of the source on the
sky can be used, again because of the availability of an
electromagnetic counterpart. We end with a summary
and conclusions.
CONSTRAINTS ON DEVIATIONS FROM THE
GENERAL-RELATIVISTIC DYNAMICS OF THE
SOURCE
Testing GR via the dynamics of a binary system in-
volves constructing a waveform model that allows for pa-
rameterized deformations away from the predictions of
GR and then constraining the associated parameters that
govern those deviations [13, 15, 16, 21–26]. For previ-
ous observations of coalescing binary black holes [13, 15],
these tests relied on the frequency domain
IMRPhenomPv2
waveform model of [27–29], which describes the inspiral,
merger, and ringdown of vacuum black holes, and pro-
vides an effective description of spin precession making
the best use of the results from analytical and numerical
relativity [30–37]. The phase evolution of this waveform
is governed by a set of coefficients
p
n
that depend on the
component masses and spins. These coefficients include
post-Newtonian (PN) parameters and phenomenological
constants that are calibrated against numerical relativity
waveforms to describe the intermediate regime between
inspiral and merger, as well as the merger-ringdown. To
test GR, the waveform model is generalized to allow for
relative deviations in each of the coefficients in turn,
i.e.
by replacing
p
n
(1 +
δ
ˆ
p
n
)
p
n
, where the
δ
ˆ
p
n
are
zero in GR. The
δ
ˆ
p
n
are then varied along with all the pa-
rameters that are also present in the case of GR (masses,
spins, and extrinsic parameters), and posterior density
functions (PDFs) are obtained using
LALInference
[38].
For GR to be correct, the value
δ
ˆ
p
n
= 0
should fall within
the support of each of the PDFs.
In this work, we modify this approach in two ways.
First, we use waveform models more suitable for bi-
nary neutron stars. Second, whereas the infrastruc-
ture [25] used to test GR with binary black holes obser-
vations [13, 15] was restricted to waveform models that
depend directly on the coefficients
p
n
, we also introduce
a new procedure that can include deviations to the phase
8
1PN
φ
n
0
.
00001
0
.
00000
0
.
00001
0
.
00002
0
.
00003
0
.
00004
δ
ˆ
φ
n
0PN
0
.
5PN
1PN
1
.
5PN
0
.
2
0
.
0
0
.
2
0
.
4
0
.
6
0
.
8
2PN
2
.
5PN
(
l
)
3PN
0
2
4
6
PhenomPNRT
SEOBNRT
3PN
(
l
)
3
.
5PN
15
10
5
0
5
FIG. 1. Posterior density functions on deviations of PN coefficients
δ
ˆ
φ
n
obtained using two different waveform models
(
PhenomPNRT
and
SEOBNRT
); see the main text for details. The
1
PN and
0
.
5PN corrections correspond to absolute devi-
ations, whereas all others represent fractional deviations from the PN coefficient in GR. The horizontal bars indicate 90%
credible regions.
1 PN
0 PN
0
.
5 PN
1 PN
1
.
5 PN
2 PN
2
.
5 PN
(
l
)
3 PN
3 PN
(
l
)
3
.
5 PN
10
5
10
4
10
3
10
2
10
1
10
0
10
1
|
ˆ
'
n
|
PhenomPNRT
SEOBNRT
FIG. 2. 90% upper bounds on deviations
|
δ
ˆ
φ
n
|
in the PN co-
efficients following from the posterior density functions shown
in Fig. 1.
evolution parameterized by
δ
ˆ
p
n
to any frequency domain
waveform model [39]. We conduct independent tests of
GR using inspiral-merger-ringdown models that incorpo-
rate deviations from GR using each of these two prescrip-
tions; by comparing these analyses, we are able to esti-
mate the magnitude of systematic modeling uncertainty
in our results.
The merger and ringdown regimes of binary neutron
stars differ from those of binary black holes, and tidal
effects not present in binary black holes need to be in-
cluded in the description of the inspiral. Significant work
has been done to understand and model the dynamics of
binary neutron stars analytically using the PN approxi-
mation to general relativity [40]. This includes modeling
the non-spinning [30, 31] and spinning radiative/inspiral
dynamics [32–37] as well as finite size effects [41–43] for
binary neutron star systems. Frequency domain wave-
forms based on the stationary phase approximation [44]
have been developed incorporating the abovementioned
effects [45–47] and have been successfully employed for
the data analysis of compact binaries. A combination of
these analytical results with the results from numerical
relativity simulations of binary neutron star mergers (see
[48] for a review) have led to the development of efficient
waveform models which account for tidal effects [49–51].
We employ the
NRTidal
models introduced in [51, 52]
as the basis of our binary neutron star waveforms: fre-
quency domain waveform models for binary black holes
are converted into waveforms for inspiraling neutron stars
that undergo tidal deformations by adding to the phase
an appropriate expression
φ
T
(
f
)
and windowing the am-
plitude such that the merger and ringdown are smoothly
removed from the model; see [52] for details. The closed-
form expression for
φ
T
(
f
)
is built by combining PN infor-
mation, the tidal effective-one-body (EOB) model of [49],
and input from numerical relativity (NR). The form of
φ
T
(
f
)
was originally obtained in a setting where the neu-
tron stars were irrotational or had their spins aligned
to the angular momentum. Nevertheless, a waveform
model that includes both tides and
precessing
spins can
be constructed by first applying
φ
T
(
f
)
to an aligned-spin
waveform, and then performing the twisting-up proce-
dure that introduces spin precession [53]. We consider
two waveform models that use this description of tidal
effects.
The first binary neutron star model we consider is con-
structed by applying this procedure to
IMRPhenomPv2
waveforms. Following the nomenclature of [19], we refer
to the resulting waveform model as
PhenomPNRT
. Param-
eterized deformations
δ
ˆ
p
n
are then introduced as shifts
in parameters describing the phase in precisely the same
way as was done for binary black holes. This will allow
us to naturally combine PDFs for the
δ
ˆ
p
n
from measure-
ments on binary black holes and binary neutron stars,
arriving at increasingly sharper results in the future. Be-
cause of the unknown merger-ringdown behavior in the
case of binary neutron stars, which in any case gets re-
moved from the waveform model, in practice only devia-
tions
δ
ˆ
φ
n
in the PN parameters
φ
n
can be bounded. The
9
set of possible testing parameters is taken to be
{
δ
ˆ
φ
2
ˆ
φ
0
ˆ
φ
1
ˆ
φ
2
ˆ
φ
3
ˆ
φ
4
ˆ
φ
(
`
)
5
ˆ
φ
6
ˆ
φ
(
`
)
6
ˆ
φ
7
}
,
(1)
where the
δ
ˆ
φ
n
are associated with powers of frequency
f
(
5+
n
)
/
3
, and
δ
ˆ
φ
(
`
)
5
and
δ
ˆ
φ
(
`
)
6
with functions
log(
f
)
and
log(
f
)
f
1
/
3
, respectively;
δ
ˆ
φ
5
would be completely de-
generate with some reference phase
φ
c
and hence is not
included in the list. In addition to corrections to the
positive PN order coefficients, deviations at
1
PN are in-
cluded because they can constrain the presence of dipole
radiation during the inspiral (discussed below). We do
not consider deviations at
0
.
5
PN order because they do
not arise from any known physical mechanism.
δ
ˆ
φ
2
and
δ
ˆ
φ
1
represent absolute rather than relative deviations, as
both are identically zero in GR.
We also employ the
SEOBNRv4
waveform model, which
is constructed from an aligned-spin EOB model for bi-
nary black holes augmented with information from NR
simulations [54]. Using the methods of [55], this model
is evaluated in the frequency domain, and then we add
the tidal correction
φ
T
(
f
)
as described above; we re-
fer to the resulting waveform model as
SEOBNRT
. Unlike
PhenomPNRT
, the
SEOBNRT
model is not constructed ex-
plicitly in terms of PN coefficients
φ
n
. Instead, we model
the effect of a relative shift
δ
ˆ
φ
n
following [39] by adding
to the frequency domain phase a term
δ
ˆ
φ
n
φ
n
f
(
5+
n
)
/
3
or
δ
ˆ
φ
(
`
)
n
φ
(
`
)
n
f
(
5+
n
)
/
3
log(
f
)
, as applicable. These cor-
rections are then tapered to zero at the merger frequency.
Fig. 1 depicts the PDFs on
δ
ˆ
φ
n
recovered when only
variations at that particular PN order are allowed. We
find that the phase evolution of GW170817 is consistent
with the GR prediction. The 90% credible region for each
parameter contains the GR value of
δ
ˆ
φ
n
= 0
at all orders
other than 3PN and 3.5PN.
1
The bounds on the positive-
PN parameters (
n
0
) obtained with GW170817 alone
are comparable to those obtained by combining the bi-
nary black hole signals GW150914, GW151226, and
GW170104 in [16] using the
IMRPhenomPv2
waveform
model. For convenience we also separately give 90% up-
per bounds on deviations in PN coefficients; see Fig. 2.
The PDFs shown in Fig. 1 were constructed using the
same choice of prior distribution outlined in [19] with the
following modifications. We use uniform priors on
δ
ˆ
φ
n
that are broad enough to fully contain the plotted PDFs.
Due to the degeneracy between
δ
ˆ
φ
0
and the chirp mass,
a broader prior distribution was chosen for the latter as
compared to in [19] for runs in which
δ
ˆ
φ
0
was allowed to
vary. All inference was done assuming the prior
|
χ
i
| ≤
0
.
99
, where
χ
i
=
c
S
i
/
(
Gm
2
i
)
is the dimensionless spin
of each body. This conservative spin prior was chosen
1
Using
PhenomPNRT
(
SEOBNRT
), the GR value lies at the 6.8-th (4.4-
th) percentile of the PDF for the 3PN parameter and at the
95.0-th (96.7-th) percentile for the 3.5PN parameter.
to allow the constraints on
δ
ˆ
φ
n
to be directly compared
with those from binary black hole observations, which
used the same prior [13, 15]. Nevertheless, throughout
this paper we assume the two objects to be neutron stars,
and following [19] we limit our prior on the component
tidal parameters to
Λ
i
5000
. (For a precise definition
of the
Λ
i
, see [1] and references therein.) This choice
was motivated by reasonable astrophysical assumptions
regarding the expected ranges for neutron star masses
and equations of state [42, 56, 57]; higher values of
Λ
are possible for some equations of state if the neutron
star masses are small (
'
0
.
9
M
). The extra freedom
introduced by including
δ
ˆ
φ
n
leads to a loss in sensitivity
in the measurement of tidal parameters; in particular,
the tail of the PDF for the tidal deformation of the less
massive body
Λ
2
touches the prior upper bound in many
of the tests. The correlation between
δ
ˆ
φ
n
and
Λ
2
means
that the upper bounds for
|
δ
ˆ
φ
n
|
would be weaker if we
did not impose our neutron star prior of
Λ
i
5000
.
Certain differences are present between the
PhenomPNRT
and
SEOBNRT
waveform models and
the way they are used. First,
PhenomPNRT
allows for
precessing spin configurations, whereas the
SEOBNRT
is
restricted to systems with spins aligned with the orbital
angular momentum. Second, continuity conditions
enforced in the construction of
PhenomPNRT
waveforms
cause deviations from GR in the inspiral to affect the
behavior of later phases of the signal, whereas the
tapering of deviations in
SEOBNRT
ensures that the
merger-ringdown of the underlying waveform is exactly
reproduced. However, this discrepancy is not expected
to affect measurements of
δ
ˆ
φ
n
significantly, because the
signal is dominated by the inspiral, and both waveform
models are amplitude-tapered near merger. Third, the
spin-induced quadrupole moment [58], which enters the
phase at
2
PN through quadrupole-monopole couplings,
is computed using neutron-star universal relations [59] in
PhenomPNRT
and is assumed to take the black-hole value
in
SEOBNRT
. Finally, in the
PhenomPNRT
model, fractional
deviations are applied only to non-spinning terms in the
PN expansion of the phase,
i.e.
terms dependent on the
bodies’ spins retain their GR values, while in
SEOBNRT
,
fractional deviations are applied to all terms at a given
post-Newtonian order. One can convert between these
two parameterizations
post hoc
by requiring that the
total phase correction be the same with either choice;
the results shown in Figs. 1 and 2 correspond to the
parameterization used by
PhenomPNRT
. Nevertheless, the
different treatment of the spin terms may still explain
the discrepancy seen at
1
.
5
PN, where spin effects first
enter. Either parameterization offers a reasonable
phenomenological description of deviations from GR;
the generally close correspondence at most PN orders
between results from the two models indicates that the
quantities measured can be interpreted in similar ways.
For more details on each waveform model we use, see
10
Table I of [19].
The long inspiral observed in GW170817 (relative to
previous binary black hole signals) allows us to place the
first stringent constraints on
δ
ˆ
φ
2
. Binaries comprised
of compact objects with additional charges that charac-
terize couplings with fields other than the metric will
generically support a time-varying dipole moment. Such
systems will emit dipole radiation in addition to the en-
ergy flux predicted in GR (given at leading order by the
quadrupole formula). Provided that this additional flux
is a small correction to the total flux, the dipole radi-
ation mainly induces a negative
1
PN order correction
in the phase evolution. Writing the total energy flux
as
F
GW
=
F
GR
(1 +
Bc
2
/v
2
)
, the leading-order modifica-
tion to the phase due to theory-agnostic effects of dipole
radiation is given by
δ
ˆ
φ
2
=
4
B/
7
[60, 61]. Combining
the PDFs shown in Fig. 1 obtained with the
PhenomPNRT
and
SEOBNRT
waveforms and restricting to the physical
parameter space
B
0
corresponding to positive outgo-
ing flux, the presence of dipole radiation in GW170817
can be constrained to
B
1
.
2
×
10
5
. For compari-
son, precise timing of radio pulses from binary pulsars
can constrain
|
B
|
<
6
×
10
8
[61]; this much stronger
constraint arises, in part, because of the much longer ob-
servation time over which the inspirals of binary pulsars
are tracked.
Though our bound on the dipole parameter
B
is weaker
than existing constraints, it is the first that comes di-
rectly from the nonlinear and dynamical regime of grav-
ity achieved during compact binary coalescences. In this
regard, we note that for general scalar-tensor theories
there are regions of parameter space where constraints
from both Solar System and binary pulsar observations
are satisfied, and yet new effects appear in the frequency
range of GW detectors, such as spontaneous scalariza-
tion [62] or resonant excitation [63, 64] of a massive field,
or dynamical scalarization [65–67].
CONSTRAINTS FROM GRAVITATIONAL WAVE
PROPAGATION
The propagation of GWs may differ in theories be-
yond GR, and the deviations depend on the distance that
the GWs travel. The search for such deviations provides
unique tests of relativity, particularly when the distance
inferred through GWs can be compared with an accu-
rate, independent distance measurement from EM obser-
vations. In GR, GWs propagate non-dispersively at the
speed of light with an amplitude inversely proportional
to the distance travelled. Using GW170817, we carry out
two different types of analyses to study the propagation
of GWs, looking for possible deviations from GR’s pre-
dictions. The first method implements a generic modifi-
cation to the GWs dispersion relation, adding terms that
correct for a massive graviton, and momentum depen-
dent dispersion that could be apparent in Lorentz vio-
lating models [68, 69]. The second modifies the distance
relation GWs follow in GR by adding correcting factors
accounting for the GW’s
gravitational leakage
into the
large extra dimensions of higher-dimensional theories of
gravity [70, 71].
Constraints on Modified Dispersion
In GR, gravitational waves propagate at the speed of
light and are non-dispersive, leading to a dispersion re-
lation
E
2
=
p
2
c
2
. An alternative theory may generi-
cally modify this as
E
2
=
p
2
c
2
+
Ap
α
c
α
, where
A
is
the coefficient of modified dispersion corresponding to
the exponent denoted by
α
[68, 69]. When
α
= 0
, a
modification with
A >
0
may be interpreted as due to
a non-zero graviton mass (
A
=
m
2
g
c
4
) [69]. It can be
shown that such modified dispersion relations would lead
to corrections to the GW phasing, thereby allowing us to
constrain any dispersion of GWs [69]. This method, im-
plemented in a Bayesian framework, placed bounds on
A
corresponding to different
α
using binary black hole
detections [16]. We apply the above method to constrain
dispersion of GWs in the case of the binary neutron star
merger GW170817 [1]. We find that GW170817 places
weaker bounds on dispersion of GWs than the binary
black holes. For instance, the bound on the graviton
mass
m
g
we obtain from GW170817 is
9
.
51
×
10
22
eV
/
c
2
,
which is weaker compared to the bounds reported in [16].
This is not surprising as GW170817 is the closest source
detected so far, and for the same SNR propagation-based
tests such as this are more effective when the sources are
farther away. This method complements the bounds on
non-dispersive standard model extension coefficients [72]
reported in [2] from GW170817.
Constraints on the Number of Spacetime
Dimensions
In higher-dimensional theories of gravity the scaling
between the GW strain and the luminosity distance of the
source is expected to be modified, suggesting a damping
of the waveform due to gravitational leakage into large
extra dimensions. This deviation from the GR scaling
h
GR
d
1
L
depends on the number of dimensions
D >
4
and would result in a systematic overestimation of the
source luminosity distance inferred from GW observa-
tions [70, 71]. A comparison of distance measurements
from GW and EM observations of GW170817 allows us
to constrain the presence of large additional spacetime
dimensions. We assume, as is the case in many extra-
dimensional models, that light and matter propagate in
four spacetime dimensions only, thus allowing us to infer
the EM luminosity distance
d
EM
L
. In the absence of a