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A Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave
Background
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
F. Acernese,
3
,
4
K. Ackley,
5
,
6
C. Adams,
7
T. Adams,
8
P. Addesso,
9
R. X. Adhikari,
1
V. B. Adya,
10
C. Affeldt,
10
M. Afrough,
11
B. Agarwal,
12
M. Agathos,
13
K. Agatsuma,
14
N. Aggarwal,
15
O. D. Aguiar,
16
L. Aiello,
17
,
18
A. Ain,
19
P. Ajith,
20
B. Allen,
10
,
21
,
22
G. Allen,
12
A. Allocca,
23
,
24
P. A. Altin,
25
A. Amato,
26
A. Ananyeva,
1
S. B. Anderson,
1
W. G. Anderson,
21
S. V. Angelova,
27
S. Antier,
28
S. Appert,
1
K. Arai,
1
M. C. Araya,
1
J. S. Areeda,
29
N. Arnaud,
28
,
30
S. Ascenzi,
31
,
32
G. Ashton,
10
M. Ast,
33
S. M. Aston,
7
P. Astone,
34
D. V. Atallah,
35
P. Aufmuth,
22
C. Aulbert,
10
K. AultONeal,
36
C. Austin,
2
A. Avila-Alvarez,
29
S. Babak,
37
P. Bacon,
38
M. K. M. Bader,
14
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
F. Barone,
3
,
4
B. Barr,
45
L. Barsotti,
15
M. Barsuglia,
38
D. Barta,
48
J. Bartlett,
46
I. Bartos,
49
,
5
R. Bassiri,
50
A. Basti,
23
,
24
J. C. Batch,
46
M. Bawaj,
51
,
42
J. C. Bayley,
45
M. Bazzan,
52
,
53
B. B
́
ecsy,
54
C. Beer,
10
M. Bejger,
55
I. Belahcene,
28
A. S. Bell,
45
B. K. Berger,
1
G. Bergmann,
10
J. J. Bero,
56
C. P. L. Berry,
57
D. Bersanetti,
58
A. Bertolini,
14
J. Betzwieser,
7
S. Bhagwat,
43
R. Bhandare,
59
I. A. Bilenko,
60
G. Billingsley,
1
C. R. Billman,
5
J. Birch,
7
R. Birney,
61
O. Birnholtz,
10
S. Biscans,
1
,
15
S. Biscoveanu,
62
,
6
A. Bisht,
22
M. Bitossi,
30
,
24
C. Biwer,
43
M. A. Bizouard,
28
J. K. Blackburn,
1
J. Blackman,
47
C. D. Blair,
1
,
63
D. G. Blair,
63
R. M. Blair,
46
S. Bloemen,
64
O. Bock,
10
N. Bode,
10
M. Boer,
65
G. Bogaert,
65
A. Bohe,
37
F. Bondu,
66
E. Bonilla,
50
R. Bonnand,
8
B. A. Boom,
14
R. Bork,
1
V. Boschi,
30
,
24
S. Bose,
67
,
19
K. Bossie,
7
Y. Bouffanais,
38
A. Bozzi,
30
C. Bradaschia,
24
P. R. Brady,
21
M. Branchesi,
17
,
18
J. E. Brau,
68
T. Briant,
69
A. Brillet,
65
M. Brinkmann,
10
V. Brisson,
28
P. Brockill,
21
J. E. Broida,
70
A. F. Brooks,
1
D. A. Brown,
43
D. D. Brown,
71
S. Brunett,
1
C. C. Buchanan,
2
A. Buikema,
15
T. Bulik,
72
H. J. Bulten,
73
,
14
A. Buonanno,
37
,
74
D. Buskulic,
8
C. Buy,
38
R. L. Byer,
50
M. Cabero,
10
L. Cadonati,
75
G. Cagnoli,
26
,
76
C. Cahillane,
1
J. Calder
́
on Bustillo,
75
T. A. Callister,
1
E. Calloni,
77
,
4
J. B. Camp,
78
M. Canepa,
79
,
58
P. Canizares,
64
K. C. Cannon,
80
H. Cao,
71
J. Cao,
81
C. D. Capano,
10
E. Capocasa,
38
F. Carbognani,
30
S. Caride,
82
M. F. Carney,
83
J. Casanueva Diaz,
28
C. Casentini,
31
,
32
S. Caudill,
21
,
14
M. Cavagli
`
a,
11
F. Cavalier,
28
R. Cavalieri,
30
G. Cella,
24
C. B. Cepeda,
1
P. Cerd
́
a-Dur
́
an,
84
G. Cerretani,
23
,
24
E. Cesarini,
85
,
32
S. J. Chamberlin,
62
M. Chan,
45
S. Chao,
86
P. Charlton,
87
E. Chase,
88
E. Chassande-Mottin,
38
D. Chatterjee,
21
B. D. Cheeseboro,
40
H. Y. Chen,
89
X. Chen,
63
Y. Chen,
47
H.-P. Cheng,
5
H. Chia,
5
A. Chincarini,
58
A. Chiummo,
30
T. Chmiel,
83
H. S. Cho,
90
M. Cho,
74
J. H. Chow,
25
N. Christensen,
70
,
65
Q. Chu,
63
A. J. K. Chua,
13
S. Chua,
69
A. K. W. Chung,
91
S. Chung,
63
G. Ciani,
5
,
52
,
53
R. Ciolfi,
92
,
93
C. E. Cirelli,
50
A. Cirone,
79
,
58
F. Clara,
46
J. A. Clark,
75
P. Clearwater,
94
F. Cleva,
65
C. Cocchieri,
11
E. Coccia,
17
,
18
P.-F. Cohadon,
69
D. Cohen,
28
A. Colla,
95
,
34
C. G. Collette,
96
L. R. Cominsky,
97
M. Constancio Jr.,
16
L. Conti,
53
S. J. Cooper,
57
P. Corban,
7
T. R. Corbitt,
2
I. Cordero-Carri
́
on,
98
K. R. Corley,
49
N. Cornish,
99
A. Corsi,
82
S. Cortese,
30
C. A. Costa,
16
E. Coughlin,
70
M. W. Coughlin,
70
,
1
S. B. Coughlin,
88
J.-P. Coulon,
65
S. T. Countryman,
49
P. Couvares,
1
P. B. Covas,
100
E. E. Cowan,
75
D. M. Coward,
63
M. J. Cowart,
7
D. C. Coyne,
1
R. Coyne,
82
J. D. E. Creighton,
21
T. D. Creighton,
101
J. Cripe,
2
S. G. Crowder,
102
T. J. Cullen,
29
,
2
A. Cumming,
45
L. Cunningham,
45
E. Cuoco,
30
T. Dal Canton,
78
G. D
́
alya,
54
S. L. Danilishin,
22
,
10
S. D’Antonio,
32
K. Danzmann,
22
,
10
A. Dasgupta,
103
C. F. Da Silva Costa,
5
V. Dattilo,
30
I. Dave,
59
M. Davier,
28
D. Davis,
43
E. J. Daw,
104
B. Day,
75
S. De,
43
D. DeBra,
50
J. Degallaix,
26
M. De Laurentis,
17
,
4
S. Del
́
eglise,
69
W. Del Pozzo,
57
,
23
,
24
N. Demos,
15
T. Denker,
10
T. Dent,
10
R. De Pietri,
105
,
106
V. Dergachev,
37
R. De Rosa,
77
,
4
R. T. DeRosa,
7
C. De Rossi,
26
,
30
R. DeSalvo,
107
O. de Varona,
10
J. Devenson,
27
S. Dhurandhar,
19
M. C. D
́
ıaz,
101
L. Di Fiore,
4
M. Di Giovanni,
108
,
93
T. Di Girolamo,
49
,
77
,
4
A. Di Lieto,
23
,
24
S. Di Pace,
95
,
34
I. Di Palma,
95
,
34
F. Di Renzo,
23
,
24
Z. Doctor,
89
V. Dolique,
26
F. Donovan,
15
K. L. Dooley,
11
S. Doravari,
10
I. Dorrington,
35
R. Douglas,
45
M. Dovale
́
Alvarez,
57
T. P. Downes,
21
M. Drago,
10
C. Dreissigacker,
10
J. C. Driggers,
46
Z. Du,
81
M. Ducrot,
8
P. Dupej,
45
S. E. Dwyer,
46
T. B. Edo,
104
M. C. Edwards,
70
A. Effler,
7
H.-B. Eggenstein,
37
,
10
P. Ehrens,
1
J. Eichholz,
1
S. S. Eikenberry,
5
R. A. Eisenstein,
15
R. C. Essick,
15
D. Estevez,
8
Z. B. Etienne,
40
T. Etzel,
1
M. Evans,
15
T. M. Evans,
7
M. Factourovich,
49
V. Fafone,
31
,
32
,
17
H. Fair,
43
S. Fairhurst,
35
X. Fan,
81
S. Farinon,
58
B. Farr,
89
W. M. Farr,
57
E. J. Fauchon-Jones,
35
M. Favata,
109
M. Fays,
35
C. Fee,
83
H. Fehrmann,
10
J. Feicht,
1
M. M. Fejer,
50
A. Fernandez-Galiana,
15
I. Ferrante,
23
,
24
E. C. Ferreira,
16
F. Ferrini,
30
F. Fidecaro,
23
,
24
D. Finstad,
43
I. Fiori,
30
D. Fiorucci,
38
M. Fishbach,
89
R. P. Fisher,
43
M. Fitz-Axen,
44
R. Flaminio,
26
,
110
M. Fletcher,
45
H. Fong,
111
J. A. Font,
84
,
112
P. W. F. Forsyth,
25
S. S. Forsyth,
75
J.-D. Fournier,
65
S. Frasca,
95
,
34
F. Frasconi,
24
Z. Frei,
54
A. Freise,
57
R. Frey,
68
V. Frey,
28
E. M. Fries,
1
P. Fritschel,
15
V. V. Frolov,
7
P. Fulda,
5
M. Fyffe,
7
H. Gabbard,
45
B. U. Gadre,
19
S. M. Gaebel,
57
J. R. Gair,
113
L. Gammaitoni,
41
M. R. Ganija,
71
S. G. Gaonkar,
19
C. Garcia-Quiros,
100
F. Garufi,
77
,
4
B. Gateley,
46
S. Gaudio,
36
G. Gaur,
114
V. Gayathri,
115
N. Gehrels
,
78
G. Gemme,
58
E. Genin,
30
A. Gennai,
24
D. George,
12
J. George,
59
L. Gergely,
116
V. Germain,
8
S. Ghonge,
75
Abhirup Ghosh,
20
Archisman Ghosh,
20
,
14
S. Ghosh,
64
,
14
,
21
J. A. Giaime,
2
,
7
K. D. Giardina,
7
A. Giazotto
,
24
arXiv:1802.10194v2 [gr-qc] 1 Mar 2018
2
K. Gill,
36
L. Glover,
107
E. Goetz,
117
R. Goetz,
5
S. Gomes,
35
B. Goncharov,
6
G. Gonz
́
alez,
2
J. M. Gonzalez Castro,
23
,
24
A. Gopakumar,
118
M. L. Gorodetsky,
60
S. E. Gossan,
1
M. Gosselin,
30
R. Gouaty,
8
A. Grado,
119
,
4
C. Graef,
45
M. Granata,
26
A. Grant,
45
S. Gras,
15
C. Gray,
46
G. Greco,
120
,
121
A. C. Green,
57
E. M. Gretarsson,
36
P. Groot,
64
H. Grote,
10
S. Grunewald,
37
P. Gruning,
28
G. M. Guidi,
120
,
121
X. Guo,
81
A. Gupta,
62
M. K. Gupta,
103
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
117
O. Halim,
18
,
17
B. R. Hall,
67
E. D. Hall,
15
E. Z. Hamilton,
35
G. Hammond,
45
M. Haney,
122
M. M. Hanke,
10
J. Hanks,
46
C. Hanna,
62
M. D. Hannam,
35
O. A. Hannuksela,
91
J. Hanson,
7
T. Hardwick,
2
J. Harms,
17
,
18
G. M. Harry,
123
I. W. Harry,
37
M. J. Hart,
45
C.-J. Haster,
111
K. Haughian,
45
J. Healy,
56
A. Heidmann,
69
M. C. Heintze,
7
H. Heitmann,
65
P. Hello,
28
G. Hemming,
30
M. Hendry,
45
I. S. Heng,
45
J. Hennig,
45
A. W. Heptonstall,
1
M. Heurs,
10
,
22
S. Hild,
45
T. Hinderer,
64
D. Hoak,
30
D. Hofman,
26
K. Holt,
7
D. E. Holz,
89
P. Hopkins,
35
C. Horst,
21
J. Hough,
45
E. A. Houston,
45
E. J. Howell,
63
A. Hreibi,
65
Y. M. Hu,
10
E. A. Huerta,
12
D. Huet,
28
B. Hughey,
36
S. Husa,
100
S. H. Huttner,
45
T. Huynh-Dinh,
7
N. Indik,
10
R. Inta,
82
G. Intini,
95
,
34
H. N. Isa,
45
J.-M. Isac,
69
M. Isi,
1
B. R. Iyer,
20
K. Izumi,
46
T. Jacqmin,
69
K. Jani,
75
P. Jaranowski,
124
S. Jawahar,
61
F. Jim
́
enez-Forteza,
100
W. W. Johnson,
2
D. I. Jones,
125
R. Jones,
45
R. J. G. Jonker,
14
L. Ju,
63
J. Junker,
10
C. V. Kalaghatgi,
35
V. Kalogera,
88
B. Kamai,
1
S. Kandhasamy,
7
G. Kang,
39
J. B. Kanner,
1
S. J. Kapadia,
21
S. Karki,
68
K. S. Karvinen,
10
M. Kasprzack,
2
M. Katolik,
12
E. Katsavounidis,
15
W. Katzman,
7
S. Kaufer,
22
K. Kawabe,
46
F. K
́
ef
́
elian,
65
D. Keitel,
45
A. J. Kemball,
12
R. Kennedy,
104
C. Kent,
35
J. S. Key,
126
F. Y. Khalili,
60
I. Khan,
17
,
32
S. Khan,
10
Z. Khan,
103
E. A. Khazanov,
127
N. Kijbunchoo,
25
Chunglee Kim,
128
J. C. Kim,
129
K. Kim,
91
W. Kim,
71
W. S. Kim,
130
Y.-M. Kim,
90
S. J. Kimbrell,
75
E. J. King,
71
P. J. King,
46
M. Kinley-Hanlon,
123
R. Kirchhoff,
10
J. S. Kissel,
46
L. Kleybolte,
33
S. Klimenko,
5
T. D. Knowles,
40
P. Koch,
10
S. M. Koehlenbeck,
10
S. Koley,
14
V. Kondrashov,
1
A. Kontos,
15
M. Korobko,
33
W. Z. Korth,
1
I. Kowalska,
72
D. B. Kozak,
1
C. Kr
̈
amer,
10
V. Kringel,
10
A. Kr
́
olak,
131
,
132
G. Kuehn,
10
P. Kumar,
111
R. Kumar,
103
S. Kumar,
20
L. Kuo,
86
A. Kutynia,
131
S. Kwang,
21
B. D. Lackey,
37
K. H. Lai,
91
M. Landry,
46
R. N. Lang,
133
J. Lange,
56
B. Lantz,
50
R. K. Lanza,
15
A. Lartaux-Vollard,
28
P. D. Lasky,
6
M. Laxen,
7
A. Lazzarini,
1
C. Lazzaro,
53
P. Leaci,
95
,
34
S. Leavey,
45
C. H. Lee,
90
H. K. Lee,
134
H. M. Lee,
135
H. W. Lee,
129
K. Lee,
45
J. Lehmann,
10
A. Lenon,
40
M. Leonardi,
108
,
93
N. Leroy,
28
N. Letendre,
8
Y. Levin,
6
T. G. F. Li,
91
S. D. Linker,
107
T. B. Littenberg,
136
J. Liu,
63
R. K. L. Lo,
91
N. A. Lockerbie,
61
L. T. London,
35
J. E. Lord,
43
M. Lorenzini,
17
,
18
V. Loriette,
137
M. Lormand,
7
G. Losurdo,
24
J. D. Lough,
10
C. O. Lousto,
56
G. Lovelace,
29
H. L
̈
uck,
22
,
10
D. Lumaca,
31
,
32
A. P. Lundgren,
10
R. Lynch,
15
Y. Ma,
47
R. Macas,
35
S. Macfoy,
27
B. Machenschalk,
10
M. MacInnis,
15
D. M. Macleod,
35
I. Maga
̃
na Hernandez,
21
F. Maga
̃
na-Sandoval,
43
L. Maga
̃
na Zertuche,
43
R. M. Magee,
62
E. Majorana,
34
I. Maksimovic,
137
N. Man,
65
V. Mandic,
44
V. Mangano,
45
G. L. Mansell,
25
M. Manske,
21
,
25
M. Mantovani,
30
F. Marchesoni,
51
,
42
F. Marion,
8
S. M
́
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49
Z. M
́
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49
C. Markakis,
12
A. S. Markosyan,
50
A. Markowitz,
1
E. Maros,
1
A. Marquina,
98
F. Martelli,
120
,
121
L. Martellini,
65
I. W. Martin,
45
R. M. Martin,
109
D. V. Martynov,
15
K. Mason,
15
E. Massera,
104
A. Masserot,
8
T. J. Massinger,
1
M. Masso-Reid,
45
S. Mastrogiovanni,
95
,
34
A. Matas,
44
F. Matichard,
1
,
15
L. Matone,
49
N. Mavalvala,
15
N. Mazumder,
67
R. McCarthy,
46
D. E. McClelland,
25
S. McCormick,
7
L. McCuller,
15
S. C. McGuire,
138
G. McIntyre,
1
J. McIver,
1
D. J. McManus,
25
L. McNeill,
6
T. McRae,
25
S. T. McWilliams,
40
D. Meacher,
62
G. D. Meadors,
37
,
10
M. Mehmet,
10
J. Meidam,
14
E. Mejuto-Villa,
9
A. Melatos,
94
G. Mendell,
46
R. A. Mercer,
21
E. L. Merilh,
46
M. Merzougui,
65
S. Meshkov,
1
C. Messenger,
45
C. Messick,
62
R. Metzdorff,
69
P. M. Meyers,
44
H. Miao,
57
C. Michel,
26
H. Middleton,
57
E. E. Mikhailov,
139
L. Milano,
77
,
4
A. L. Miller,
5
,
95
,
34
B. B. Miller,
88
J. Miller,
15
M. Millhouse,
99
M. C. Milovich-Goff,
107
O. Minazzoli,
65
,
140
Y. Minenkov,
32
J. Ming,
37
C. Mishra,
141
S. Mitra,
19
V. P. Mitrofanov,
60
G. Mitselmakher,
5
R. Mittleman,
15
D. Moffa,
83
A. Moggi,
24
K. Mogushi,
11
M. Mohan,
30
S. R. P. Mohapatra,
15
M. Montani,
120
,
121
C. J. Moore,
13
D. Moraru,
46
G. Moreno,
46
S. R. Morriss,
101
B. Mours,
8
C. M. Mow-Lowry,
57
G. Mueller,
5
A. W. Muir,
35
Arunava Mukherjee,
10
D. Mukherjee,
21
S. Mukherjee,
101
N. Mukund,
19
A. Mullavey,
7
J. Munch,
71
E. A. Mu
̃
niz,
43
M. Muratore,
36
P. G. Murray,
45
K. Napier,
75
I. Nardecchia,
31
,
32
L. Naticchioni,
95
,
34
R. K. Nayak,
142
J. Neilson,
107
G. Nelemans,
64
,
14
T. J. N. Nelson,
7
M. Nery,
10
A. Neunzert,
117
L. Nevin,
1
J. M. Newport,
123
G. Newton
,
45
K. K. Y. Ng,
91
T. T. Nguyen,
25
D. Nichols,
64
A. B. Nielsen,
10
S. Nissanke,
64
,
14
A. Nitz,
10
A. Noack,
10
F. Nocera,
30
D. Nolting,
7
C. North,
35
L. K. Nuttall,
35
J. Oberling,
46
G. D. O’Dea,
107
G. H. Ogin,
143
J. J. Oh,
130
S. H. Oh,
130
F. Ohme,
10
M. A. Okada,
16
M. Oliver,
100
P. Oppermann,
10
Richard J. Oram,
7
B. O’Reilly,
7
R. Ormiston,
44
L. F. Ortega,
5
R. O’Shaughnessy,
56
S. Ossokine,
37
D. J. Ottaway,
71
H. Overmier,
7
B. J. Owen,
82
A. E. Pace,
62
J. Page,
136
M. A. Page,
63
A. Pai,
115
,
144
S. A. Pai,
59
J. R. Palamos,
68
O. Palashov,
127
C. Palomba,
34
A. Pal-Singh,
33
Howard Pan,
86
Huang-Wei Pan,
86
B. Pang,
47
P. T. H. Pang,
91
C. Pankow,
88
F. Pannarale,
35
B. C. Pant,
59
F. Paoletti,
24
A. Paoli,
30
M. A. Papa,
37
,
21
,
10
A. Parida,
19
W. Parker,
7
D. Pascucci,
45
A. Pasqualetti,
30
R. Passaquieti,
23
,
24
D. Passuello,
24
M. Patil,
132
B. Patricelli,
145
,
24
B. L. Pearlstone,
45
M. Pedraza,
1
R. Pedurand,
26
,
146
L. Pekowsky,
43
A. Pele,
7
S. Penn,
147
C. J. Perez,
46
A. Perreca,
1
,
108
,
93
L. M. Perri,
88
H. P. Pfeiffer,
111
,
37
M. Phelps,
45
O. J. Piccinni,
95
,
34
M. Pichot,
65
F. Piergiovanni,
120
,
121
V. Pierro,
9
G. Pillant,
30
L. Pinard,
26
I. M. Pinto,
9
M. Pirello,
46
M. Pitkin,
45
M. Poe,
21
R. Poggiani,
23
,
24
3
P. Popolizio,
30
E. K. Porter,
38
A. Post,
10
J. Powell,
148
J. Prasad,
19
J. W. W. Pratt,
36
G. Pratten,
100
V. Predoi,
35
T. Prestegard,
21
M. Prijatelj,
10
M. Principe,
9
S. Privitera,
37
G. A. Prodi,
108
,
93
L. G. Prokhorov,
60
O. Puncken,
10
M. Punturo,
42
P. Puppo,
34
M. P
̈
urrer,
37
H. Qi,
21
V. Quetschke,
101
E. A. Quintero,
1
R. Quitzow-James,
68
F. J. Raab,
46
D. S. Rabeling,
25
H. Radkins,
46
P. Raffai,
54
S. Raja,
59
C. Rajan,
59
B. Rajbhandari,
82
M. Rakhmanov,
101
K. E. Ramirez,
101
A. Ramos-Buades,
100
P. Rapagnani,
95
,
34
V. Raymond,
37
M. Razzano,
23
,
24
J. Read,
29
T. Regimbau,
65
L. Rei,
58
S. Reid,
61
D. H. Reitze,
1
,
5
W. Ren,
12
S. D. Reyes,
43
F. Ricci,
95
,
34
P. M. Ricker,
12
S. Rieger,
10
K. Riles,
117
M. Rizzo,
56
N. A. Robertson,
1
,
45
R. Robie,
45
F. Robinet,
28
A. Rocchi,
32
L. Rolland,
8
J. G. Rollins,
1
V. J. Roma,
68
R. Romano,
3
,
4
C. L. Romel,
46
J. H. Romie,
7
D. Rosi
́
nska,
149
,
55
M. P. Ross,
150
S. Rowan,
45
A. R
̈
udiger,
10
P. Ruggi,
30
G. Rutins,
27
K. Ryan,
46
S. Sachdev,
1
T. Sadecki,
46
L. Sadeghian,
21
M. Sakellariadou,
151
L. Salconi,
30
M. Saleem,
115
F. Salemi,
10
A. Samajdar,
142
L. Sammut,
6
L. M. Sampson,
88
E. J. Sanchez,
1
L. E. Sanchez,
1
N. Sanchis-Gual,
84
V. Sandberg,
46
J. R. Sanders,
43
B. Sassolas,
26
P. R. Saulson,
43
O. Sauter,
117
R. L. Savage,
46
A. Sawadsky,
33
P. Schale,
68
M. Scheel,
47
J. Scheuer,
88
J. Schmidt,
10
P. Schmidt,
1
,
64
R. Schnabel,
33
R. M. S. Schofield,
68
A. Sch
̈
onbeck,
33
E. Schreiber,
10
D. Schuette,
10
,
22
B. W. Schulte,
10
B. F. Schutz,
35
,
10
S. G. Schwalbe,
36
J. Scott,
45
S. M. Scott,
25
E. Seidel,
12
D. Sellers,
7
A. S. Sengupta,
152
D. Sentenac,
30
V. Sequino,
31
,
32
,
17
A. Sergeev,
127
D. A. Shaddock,
25
T. J. Shaffer,
46
A. A. Shah,
136
M. S. Shahriar,
88
M. B. Shaner,
107
L. Shao,
37
B. Shapiro,
50
P. Shawhan,
74
A. Sheperd,
21
D. H. Shoemaker,
15
D. M. Shoemaker,
75
K. Siellez,
75
X. Siemens,
21
M. Sieniawska,
55
D. Sigg,
46
A. D. Silva,
16
L. P. Singer,
78
A. Singh,
37
,
10
,
22
A. Singhal,
17
,
34
A. M. Sintes,
100
B. J. J. Slagmolen,
25
B. Smith,
7
J. R. Smith,
29
R. J. E. Smith,
1
,
6
S. Somala,
153
E. J. Son,
130
J. A. Sonnenberg,
21
B. Sorazu,
45
F. Sorrentino,
58
T. Souradeep,
19
A. P. Spencer,
45
A. K. Srivastava,
103
K. Staats,
36
A. Staley,
49
M. Steinke,
10
J. Steinlechner,
33
,
45
S. Steinlechner,
33
D. Steinmeyer,
10
S. P. Stevenson,
57
,
148
R. Stone,
101
D. J. Stops,
57
K. A. Strain,
45
G. Stratta,
120
,
121
S. E. Strigin,
60
A. Strunk,
46
R. Sturani,
154
A. L. Stuver,
7
T. Z. Summerscales,
155
L. Sun,
94
S. Sunil,
103
J. Suresh,
19
P. J. Sutton,
35
B. L. Swinkels,
30
M. J. Szczepa
́
nczyk,
36
M. Tacca,
14
S. C. Tait,
45
C. Talbot,
6
D. Talukder,
68
D. B. Tanner,
5
D. Tao,
70
M. T
́
apai,
116
A. Taracchini,
37
J. D. Tasson,
70
J. A. Taylor,
136
R. Taylor,
1
S. V. Tewari,
147
T. Theeg,
10
F. Thies,
10
E. G. Thomas,
57
M. Thomas,
7
P. Thomas,
46
K. A. Thorne,
7
E. Thrane,
6
S. Tiwari,
17
,
93
V. Tiwari,
35
K. V. Tokmakov,
61
K. Toland,
45
M. Tonelli,
23
,
24
Z. Tornasi,
45
A. Torres-Forn
́
e,
84
C. I. Torrie,
1
D. T
̈
oyr
̈
a,
57
F. Travasso,
30
,
42
G. Traylor,
7
J. Trinastic,
5
M. C. Tringali,
108
,
93
L. Trozzo,
156
,
24
K. W. Tsang,
14
M. Tse,
15
R. Tso,
1
L. Tsukada,
80
D. Tsuna,
80
D. Tuyenbayev,
101
K. Ueno,
21
D. Ugolini,
157
C. S. Unnikrishnan,
118
A. L. Urban,
1
S. A. Usman,
35
H. Vahlbruch,
22
G. Vajente,
1
G. Valdes,
2
N. van Bakel,
14
M. van Beuzekom,
14
J. F. J. van den Brand,
73
,
14
C. Van Den Broeck,
14
,
158
D. C. Vander-Hyde,
43
L. van der Schaaf,
14
J. V. van Heijningen,
14
A. A. van Veggel,
45
M. Vardaro,
52
,
53
V. Varma,
47
S. Vass,
1
M. Vas
́
uth,
48
A. Vecchio,
57
G. Vedovato,
53
J. Veitch,
45
P. J. Veitch,
71
K. Venkateswara,
150
G. Venugopalan,
1
D. Verkindt,
8
F. Vetrano,
120
,
121
A. Vicer
́
e,
120
,
121
A. D. Viets,
21
S. Vinciguerra,
57
D. J. Vine,
27
J.-Y. Vinet,
65
S. Vitale,
15
T. Vo,
43
H. Vocca,
41
,
42
C. Vorvick,
46
S. P. Vyatchanin,
60
A. R. Wade,
1
L. E. Wade,
83
M. Wade,
83
R. Walet,
14
M. Walker,
29
L. Wallace,
1
S. Walsh,
37
,
10
,
21
G. Wang,
17
,
121
H. Wang,
57
J. Z. Wang,
62
W. H. Wang,
101
Y. F. Wang,
91
R. L. Ward,
25
J. Warner,
46
M. Was,
8
J. Watchi,
96
B. Weaver,
46
L.-W. Wei,
10
,
22
M. Weinert,
10
A. J. Weinstein,
1
R. Weiss,
15
L. Wen,
63
E. K. Wessel,
12
P. Weßels,
10
J. Westerweck,
10
T. Westphal,
10
K. Wette,
25
J. T. Whelan,
56
B. F. Whiting,
5
C. Whittle,
6
D. Wilken,
10
D. Williams,
45
R. D. Williams,
1
A. R. Williamson,
64
J. L. Willis,
1
,
159
B. Willke,
22
,
10
M. H. Wimmer,
10
W. Winkler,
10
C. C. Wipf,
1
H. Wittel,
10
,
22
G. Woan,
45
J. Woehler,
10
J. Wofford,
56
K. W. K. Wong,
91
J. Worden,
46
J. L. Wright,
45
D. S. Wu,
10
D. M. Wysocki,
56
S. Xiao,
1
H. Yamamoto,
1
C. C. Yancey,
74
L. Yang,
160
M. J. Yap,
25
M. Yazback,
5
Hang Yu,
15
Haocun Yu,
15
M. Yvert,
8
A. Zadro
̇
zny,
131
M. Zanolin,
36
T. Zelenova,
30
J.-P. Zendri,
53
M. Zevin,
88
L. Zhang,
1
M. Zhang,
139
T. Zhang,
45
Y.-H. Zhang,
56
C. Zhao,
63
M. Zhou,
88
Z. Zhou,
88
S. J. Zhu,
37
,
10
X. J. Zhu,
6
M. E. Zucker,
1
,
15
and J. Zweizig
1
(LIGO Scientific Collaboration and Virgo Collaboration)
Deceased, February 2017.
Deceased, November 2017.
Deceased, December 2016.
1
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2
Louisiana State University, Baton Rouge, LA 70803, USA
3
Universit
`
a di Salerno, Fisciano, I-84084 Salerno, Italy
4
INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
5
University of Florida, Gainesville, FL 32611, USA
6
OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia
7
LIGO Livingston Observatory, Livingston, LA 70754, USA
8
Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),
Universit
́
e Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France
9
University of Sannio at Benevento, I-82100 Benevento,
Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
10
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany
4
11
The University of Mississippi, University, MS 38677, USA
12
NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
13
University of Cambridge, Cambridge CB2 1TN, United Kingdom
14
Nikhef, Science Park, 1098 XG Amsterdam, The Netherlands
15
LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
16
Instituto Nacional de Pesquisas Espaciais, 12227-010 S
̃
ao Jos
́
e dos Campos, S
̃
ao Paulo, Brazil
17
Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy
18
INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy
19
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
20
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
21
University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
22
Leibniz Universit
̈
at Hannover, D-30167 Hannover, Germany
23
Universit
`
a di Pisa, I-56127 Pisa, Italy
24
INFN, Sezione di Pisa, I-56127 Pisa, Italy
25
OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia
26
Laboratoire des Mat
́
eriaux Avanc
́
es (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France
27
SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
28
LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit
́
e Paris-Saclay, F-91898 Orsay, France
29
California State University Fullerton, Fullerton, CA 92831, USA
30
European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
31
Universit
`
a di Roma Tor Vergata, I-00133 Roma, Italy
32
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
33
Universit
̈
at Hamburg, D-22761 Hamburg, Germany
34
INFN, Sezione di Roma, I-00185 Roma, Italy
35
Cardiff University, Cardiff CF24 3AA, United Kingdom
36
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
37
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany
38
APC, AstroParticule et Cosmologie, Universit
́
e Paris Diderot, CNRS/IN2P3, CEA/Irfu,
Observatoire de Paris, Sorbonne Paris Cit
́
e, F-75205 Paris Cedex 13, France
39
Korea Institute of Science and Technology Information, Daejeon 34141, Korea
40
West Virginia University, Morgantown, WV 26506, USA
41
Universit
`
a 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 Mikl
́
os
́
ut 29-33, Hungary
49
Columbia University, New York, NY 10027, USA
50
Stanford University, Stanford, CA 94305, USA
51
Universit
`
a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
52
Universit
`
a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
53
INFN, Sezione di Padova, I-35131 Padova, Italy
54
Institute of Physics, E
̈
otv
̈
os University, P
́
azm
́
any P. s. 1/A, Budapest 1117, Hungary
55
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland
56
Rochester Institute of Technology, Rochester, NY 14623, USA
57
University of Birmingham, Birmingham B15 2TT, United Kingdom
58
INFN, Sezione di Genova, I-16146 Genova, Italy
59
RRCAT, Indore MP 452013, India
60
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
61
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
62
The Pennsylvania State University, University Park, PA 16802, USA
63
OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia
64
Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
65
Artemis, Universit
́
e C
ˆ
ote d’Azur, Observatoire C
ˆ
ote d’Azur, CNRS, CS 34229, F-06304 Nice Cedex 4, France
66
Institut FOTON, CNRS, Universit
́
e de Rennes 1, F-35042 Rennes, France
67
Washington State University, Pullman, WA 99164, USA
68
University of Oregon, Eugene, OR 97403, USA
69
Laboratoire Kastler Brossel, UPMC-Sorbonne Universit
́
es, CNRS,
ENS-PSL Research University, Coll
`
ege de France, F-75005 Paris, France
70
Carleton College, Northfield, MN 55057, USA
71
OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia
72
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
5
73
VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
74
University of Maryland, College Park, MD 20742, USA
75
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
76
Universit
́
e Claude Bernard Lyon 1, F-69622 Villeurbanne, France
77
Universit
`
a di Napoli ‘Federico II,’ Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
78
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
79
Dipartimento di Fisica, Universit
`
a degli Studi di Genova, I-16146 Genova, Italy
80
RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.
81
Tsinghua University, Beijing 100084, China
82
Texas Tech University, Lubbock, TX 79409, USA
83
Kenyon College, Gambier, OH 43022, USA
84
Departamento de Astronom
́
ıa y Astrof
́
ısica, Universitat de Val
`
encia, E-46100 Burjassot, Val
`
encia, Spain
85
Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, I-00184 Roma, Italy
86
National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
87
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
88
Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA
89
University of Chicago, Chicago, IL 60637, USA
90
Pusan National University, Busan 46241, Korea
91
The Chinese University of Hong Kong, Shatin, NT, Hong Kong
92
INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy
93
INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
94
OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia
95
Universit
`
a di Roma ‘La Sapienza,’ I-00185 Roma, Italy
96
Universit
́
e Libre de Bruxelles, Brussels 1050, Belgium
97
Sonoma State University, Rohnert Park, CA 94928, USA
98
Departamento de Matem
́
aticas, Universitat de Val
`
encia, E-46100 Burjassot, Val
`
encia, Spain
99
Montana State University, Bozeman, MT 59717, USA
100
Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
101
The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
102
Bellevue College, Bellevue, WA 98007, USA
103
Institute for Plasma Research, Bhat, Gandhinagar 382428, India
104
The University of Sheffield, Sheffield S10 2TN, United Kingdom
105
Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit
`
a di Parma, I-43124 Parma, Italy
106
INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy
107
California State University, Los Angeles, 5151 State University Dr, Los Angeles, CA 90032, USA
108
Universit
`
a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
109
Montclair State University, Montclair, NJ 07043, USA
110
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
111
Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada
112
Observatori Astron
`
omic, Universitat de Val
`
encia, E-46980 Paterna, Val
`
encia, Spain
113
School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
114
University and Institute of Advanced Research, Koba Institutional Area, Gandhinagar Gujarat 382007, India
115
IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
116
University of Szeged, D
́
om t
́
er 9, Szeged 6720, Hungary
117
University of Michigan, Ann Arbor, MI 48109, USA
118
Tata Institute of Fundamental Research, Mumbai 400005, India
119
INAF, Osservatorio Astronomico di Capodimonte, I-80131, Napoli, Italy
120
Universit
`
a degli Studi di Urbino ‘Carlo Bo,’ I-61029 Urbino, Italy
121
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
122
Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
123
American University, Washington, D.C. 20016, USA
124
University of Białystok, 15-424 Białystok, Poland
125
University of Southampton, Southampton SO17 1BJ, United Kingdom
126
University of Washington Bothell, 18115 Campus Way NE, Bothell, WA 98011, USA
127
Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
128
Korea Astronomy and Space Science Institute, Daejeon 34055, Korea
129
Inje University Gimhae, South Gyeongsang 50834, Korea
130
National Institute for Mathematical Sciences, Daejeon 34047, Korea
131
NCBJ, 05-400
́
Swierk-Otwock, Poland
132
Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland
133
Hillsdale College, Hillsdale, MI 49242, USA
134
Hanyang University, Seoul 04763, Korea
135
Seoul National University, Seoul 08826, Korea
136
NASA Marshall Space Flight Center, Huntsville, AL 35811, USA
6
137
ESPCI, CNRS, F-75005 Paris, France
138
Southern University and A&M College, Baton Rouge, LA 70813, USA
139
College of William and Mary, Williamsburg, VA 23187, USA
140
Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco
141
Indian Institute of Technology Madras, Chennai 600036, India
142
IISER-Kolkata, Mohanpur, West Bengal 741252, India
143
Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA
144
Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076, India
145
Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
146
Universit
́
e de Lyon, F-69361 Lyon, France
147
Hobart and William Smith Colleges, Geneva, NY 14456, USA
148
OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia
149
Janusz Gil Institute of Astronomy, University of Zielona G
́
ora, 65-265 Zielona G
́
ora, Poland
150
University of Washington, Seattle, WA 98195, USA
151
King’s College London, University of London, London WC2R 2LS, United Kingdom
152
Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
153
Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India
154
International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil
155
Andrews University, Berrien Springs, MI 49104, USA
156
Universit
`
a di Siena, I-53100 Siena, Italy
157
Trinity University, San Antonio, TX 78212, USA
158
Van Swinderen Institute for Particle Physics and Gravity,
University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
159
Abilene Christian University, Abilene, TX 79699, USA
160
Colorado State University, Fort Collins, CO 80523, USA
(Dated: March 5, 2018)
The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of
general relativity, including direct study of the polarization of gravitational waves. While general relativity
allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two
vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of
the stochastic gravitational-wave background, formed by the superposition of cosmological and individually-
unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we
search for a stochastic background of generically-polarized gravitational waves. We find no evidence for a
background of any polarization, and place the first direct bounds on the contributions of vector and scalar
polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we
limit the energy-densities of tensor, vector, and scalar modes at 95% credibility to
T
0
<
5
.
6
×
10
8
,
V
0
<
6
.
4
×
10
8
, and
S
0
<
1
.
1
×
10
7
at a reference frequency
f
0
= 25
Hz.
Introduction
– The direct detection of gravitational waves
offers novel opportunities to test general relativity in previ-
ously unexplored regimes. Already, the compact binary merg-
ers [1–5] observed by Advanced LIGO (the Laser Interfer-
ometer Gravitational Wave Observatory) [6, 7] and Advanced
Virgo [8] have enabled improved limits on the graviton mass,
experimental measurements of post-Newtonian parameters,
and inference of the speed of gravitational waves, among other
tests [3, 9–11].
Another central prediction of general relativity is the exis-
tence of only two gravitational-wave polarizations (the tensor
plus and cross modes). Generic metric theories of gravity,
however, can allow for up to four additional polarizations: the
x
and
y
vector modes and the breathing and longitudinal scalar
modes [12–14]. The observation of vector or scalar modes
would be in direct conflict with general relativity, and so the
direct measurement of gravitational-wave polarizations offers
a promising avenue by which to test theories of gravity [14].
Recently, the Advanced LIGO-Virgo network has suc-
ceeded in making the first direct statement about the polar-
ization of gravitational waves. The gravitational-wave sig-
nal GW170814, observed by both the Advanced LIGO and
Virgo detectors, significantly favored a model assuming pure
tensor polarization over models with pure vector or scalar
polarizations [4, 15].
In general, however, the ability of
the Advanced LIGO-Virgo network to study the polariza-
tion of gravitational-wave transients is limited by several fac-
tors. First, the LIGO-Hanford and LIGO-Livingston detec-
tors are nearly co-oriented, preventing Advanced LIGO from
sensitively measuring more than a single polarization mode
[4, 9, 10, 15]. Second, at least five detectors are needed to
fully characterize the five polarization degrees of freedom ac-
cessible to quadrupole detectors. Quadrupole detectors (those
measuring differential arm motion) have degenerate responses
to breathing and longitudinal modes, and can therefore mea-
sure only a single linear combination of scalar breathing and
longitudinal polarizations [14–17].
Beyond compact binary mergers, another target for Ad-
vanced LIGO and Virgo is the stochastic gravitational-wave
background. An astrophysical stochastic background is ex-
pected to arise from the population of distant compact bi-
nary mergers [18–23], core-collapse supernovae [24–26], and