arXiv:2001.09793v3 [gr-qc] 27 Apr 2020
Prospects for Fundamental Physics with LISA
Enrico Barausse,
1, 2
Emanuele Berti,
3
Thomas Hertog,
4
Scott A. Hughes ,
5
Philippe Jetzer,
6
Paolo
Pani,
7
Thomas P. Sotiriou,
8
Nicola Tamanini,
9
Helvi Witek,
10
Kent Yag i,
11
and Nicol´as Yunes
12
1
SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN Sezione di Trieste,
and IFPU - Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
2
CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis Bd Arago, 75014 Paris, France.
3
Department of Physics and A stronomy, Johns Hopkins University,
3400 N. Charles Street, Baltimore, Maryland 21218, US
4
Institute for Theoretical Physics, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.
5
Department of Physics and Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U SA.
6
Physik-Institut, Universit¨at Z¨urich, Wi nterthurerstrasse 190, 8057 Zu¨rich, Switzerland.
7
Dipartimento di Fisica, “Sapienza” Universit`a di Roma & Sezione INFN Roma1, Piazzale Aldo Moro 5, 00185, Roma, Italy.
8
School of Mathematical Sciences & School of Physics and Astronomy,
University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom.
9
Max-Planck-Institut f¨ur Gravitationsphysik, Albert-Einstein-Institut,
Am M¨uhlenberg 1, 14476 Potsdam-Golm, Germany.
10
Department of Physics, King’s College London, The Strand, WC2R 2LS, London,
UK and Department of Physics and University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
11
Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA.
12
eXtreme Gravity Institute, Department of Physics,
Montana State University, Bozeman, MT 59717,
United States and University of Ill inois at Urbana-Champaign, Urbana, Illinois 61801, USA.
T. Abdelsalhin
1
, A. Achucarro
2
, K. V. Aelst
3
, N.
Afshordi
4
, S. Akcay
5
, L. Annulli
69
, K. G. Arun
7
, I.
Ayuso
132
, V. Baibhav
9
, T. Baker
10
, H. Bantilan
10
,
T. Barreir o
12
, C. Barrer a-Hinojosa
13
, N. Bartolo
14
, D.
Baumann
15
, E. Belgacem
16
, E. Bellini
17
, N. Bellomo
18
, I.
Ben-Dayan
19
, I. Bena
20
, R. Benkel
21
, E. Bergshoefs
22
, L.
Bernard
6
, S. Bernuzzi
5
, D. Bertacca
14
, M. Besancon
24
,
F. B e utler
25
, F. Beyer
26
, S. Bhagwat
1
, J. Bicak
27
,
S. B iondini
28
, S. Bize
29
, D. Blas
30
, C. Boehmer
31
,
K. Boller
32
, B. Bonga
4
, C. Bonvin
16
, P. Boss o
33
, G.
Bozzola
34
, P. Brax
20
, M. Breitbach
35
, R. Brito
1
, M.
Bruni
25
, B. Br¨ugmann
5
, H. Bulten
36
, A. Buonanno
21
, A.
O. Burke
37
, L. M. Bur ko
38
, C. Burrage
126
, F. Cabral
12
,
G. Calcagni
39
, C. Caprini
21
, A. C´ardenas-Avenda˜no
42
,
M. Celoria
41
, K. Chatziioannou
123
, D. Chernoff
44
, K.
Clough
17
, A. Coates
45
, D. Comelli
41
, G. Comp`ere
46
,
D. Croon
111
, D. Cruces
18
, G. Cusin
17
, C. Dalang
16
,
U. Da nie lsson
47
, S. Das
33
, S. Da tta
23
, J. de Boer
40
,
V. De Luca
16
, C. De Rham
48
, V. Desjacques
122
,
K. Destounis
49
, F. Di Filippo
117
, A. Dima
117
, E.
Dimastrogiovanni
50
, S. Dolan
51
, D. Doneva
45
, F.
Duque
49
, R. Durrer
16
, W. East
4
, R. Easther
52
, M.
Elley
30
, J. R. Ellis
30
, R. Emparan
18
, J.M. Ezquiaga
114
,
M. Fairbairn
30
, S. Fairhurst
53
, H. F. Farmer
54
, M. R.
Fasiello
55
, V. Ferrari
1
, P. G. Fe rreira
17
, G. Ficarra
30
,
P. Figueras
10
, S. Fisenko
56
, S. Foffa
16
, N. Fr anchini
117
,
G. Franciolini
16
, K. Fransen
125
, J. Frauendiener
26
, N.
Frusciante
12
, R. Fujita
57
, J. Gair
37
, A. Ganz
14
, P.
Garcia
6
, J . Garcia-Bellido
108
, J . Garriga
18
, R. Geiger
29
,
C. Geng
58
, L.
´
A. Gergely
59
, C. Germani
18
, D. Gerosa
60
,
S.B. Giddings
124
, E. Gourgoulhon
3
, P. Grandclement
3
,
L. Graziani
1
, L. Gualtieri
1
, D. Haggard
61
, S. Haino
62
,
R. Halburd
31
, W.-B. Han
63
, A. J. Hawken
64
, A. Hees
29
,
I. S. Heng
65
, J. Hennig
26
, C. Herdeiro
120
, S. Hervik
66
,
J. v. Ho lten
36
, C. J. D. Hoyle
67
, Y. Hu
31
, M. Hull
25
, T.
Ikeda
6
, M. Isi
68
, A. Jenkins
30
, F. Juli´e
9
, E . Kajfasz
64
,
C. Kalaghatgi
53
, N. Kalope r
70
, M. Kamionkowski
9
, V.
Karas
27
, S. Ka stha
7
, Z. Ke resztes
59
, L. Kidder
71
, T.
Kimpson
31
, A. Klein
119
, S. Klione r
72
, K. K okkotas
45
, H.
Kolesova
66
, S. Kolkowitz
73
, J. Kopp
35
, K. Koyama
25
,
N. V. Krishnendu
7
, J. A. V. Kroon
10
, M. Kunz
16
,
O. Lahav
31
, A. Landragin
29
, R.N. Lang
74
, C. Le
Poncin-Lafitte
29
, J. Lemos
6
, B. Li
13
, S. Liberati
117
,
M. Liguori
14
, F. Lin
75
, G. Liu
76
, F.S.N. Lobo
12
, R.
Loll
22
, L. Lombriser
16
, G. Lovelace
77
, R. P. Macedo
10
,
E. Madge
35
, E. Maggio
1
, M. Maggiore
16
, S. Marassi
1
,
P. Marcoccia
66
, C. Markakis
10
, W. Martens
115
, K.
Martinovic
30
, C.J.A.P. Martins
84
, A. Maselli
1
, S.
Mastrogiovanni
118
, S. Matarrese
14
, A. Matas
21
, N. E.
Mavromatos
30
, A. Mazumdar
112
, P. D. Meerburg
28
, E.
Megias
78
, J. Mille r
17
, J. P. Mimoso
12
, L. Mittnacht
35
,
M. M. Montero
46
, B. Moore
79
, P. Martin-Moruno
80
,
I. Musco
16,18
, H. Nakano
81
, S. Na mpalliwar
45
, G.
Nardini
66
, A. Nielsen
66
, J. Nov´ak
82
, N.J . Nunes
12
,
M. Okounkova
43
, R. Oliveri
27
, F. Oppizzi
14
, G.
Orlando
14
, N. Oshita
4
, G. Pappas
83
, V. Paschalidis
34
,
H. Peiris
31
, M. Peloso
14
, S. Perkins
42
, V. Pettorino
24
,
I. Pikovski
85
, L. Pilo
41
, J. Podolsky
27
, A. Pontzen
31
, S.
Prabhat
1
, G. Pratten
60
, T. Prokopec
86
, M. Prouza
27
,
H. Qi
53
, A. Raccanelli
127
, A. Rajantie
48
, L. Randall
87
,
G. Raposo
1
, V. Raymond
53
, S. Renaux-Petel
11
, A.
Ricciardone
128
, A. Riotto
16
, T. Robson
79
, D. Roest
28
,
R. Ro llo
41
, S. Rosofsky
88
, J. J. Ruan
61
, D. Rubiera-
Garc´ıa
12,80
, M. Ruiz
42
, M. Rusu
89
, F. Sabatie
24
, N.
Sago
90
, M. Sakellariadou
30
, I. D. Saltas
27
, L. Sberna
4
,
B. Sathyaprakash
53
, M. Scheel
43
, P. Schmidt
60
, B.
2
Schutz
21
, P. Schwaller
35
, L. Shao
91
, S. L. Shapiro
42
,
D. Shoemaker
92
, A. d. Silva
12
, C. Simpson
37
, C.
F. Sopuerta
93
, A. Spallicci
95
, B.A. Stefanek
35
, L.
Stein
43
, N. Stergioulas
83
, M. Stott
30
, P. Sutton
53
, R.
Svarc
27
, H. Tagoshi
96
, T. Tahamtan
27
, H. Takeda
97
, T.
Tanaka
98
, G. Tantilian
83
, G. Tasinato
130
, O. Tattersall
17
,
S. Teukolsky
71
, A. L. Tiec
3
, G. Theureau
109
, M.
Trodden
110
, A. Tolley
48
, A. Toubiana
99
, D. Traykova
17
,
A. Tsokaros
42
, C. Unal
100
, C. S. Unnikrishnan
101
, E. C.
Vagenas
131
, P. Valageas
20
, M. Va llisneri
43
, J. Van den
Brand
36
, C. Van den Broeck
36
, M. van de Mee nt
116
, P.
Vanhove
20
, V. Varma
43
, J. Veitch
65
, B . Vercnocke
46
,
L. Verde
18
, D. Vernieri
12
, F. Vernizz i
20
, R. Vicente
6
,
F. Vidotto
129
, M. Viss e r
121
, Z. Vlah
14
, S. Vretinaris
83
,
S. V¨olkel
45,117
, Q. Wang
4
, Yu-Tong Wang
113
, M. C.
Werner
102
, J. Westernacher
34
, R. v. d. Weygaert
28
, D.
Wiltshire
104
, T. Wiseman
48
, P. Wolf
29
, K. Wu
31
, K.
Yamada
98
, H. Yang
4
, L. Yi
43
, X. Yue
63
, D. Yvon
24
, M.
Zilh˜ao
6
, A. Zimmer man
106
, M. Zumalacarregui
107
,
1
Dipartimento di Fi sica, “Sapienza” Universit`a di Roma & Sezione
INFN R oma1, Piazzale Aldo Moro 5, 00185, Roma, Italy.
2
LISA NL Group, University of Leiden, Netherland
3
Laboratoire Univers et Theories, France
4
Perimeter, Canada
5
University of Jena Relativity Group, Germany
6
LUTH, Observatoire de Paris, France
7
Chennai Mathematical Institute, India
8
eXtreme Gravity Institute, Montana State University,Illinois
Relativity Group, USA
9
Department of Physics and Astronomy, Johns Hopkins U niver-
sity, 3400 N. Charles Street, Baltimore, Maryland 21218, US
10
Queen Mary University of London, UK
11
Institut d’As tr ophysique de Paris, France
12
Instituto de Astrof´ısica e Ciˆencias do Espaco, Lisboa, Portugal
13
ICC Durham, UK
14
Dipartimento di Fi sica e Astronomia Galileo Galilei, Universit`a
di Padova, 35131 Padova Italy and INFN, Sezione di Padova,
35131 Padova Italy
15
LISA NL Group, UvA, Netherland
16
D´epartement de Physique Th´eorique and Center for Astropar-
ticle Physics, Universit´e de Gen`eve, 24 quai Ansermet, CH–1211
Gen`eve 4, Switzerland
17
Astrophysics, University of Oxford, Oxford OX1 3RH, UK
18
Institut de Ci`encies del Cosmos, Universitat de Barcelona, Mart´ı
i Franqu`es 1, 08028 B arcelona, Spain
19
Ariel Early Universe Physics
20
Institut de physique th´eorique, Universit´e Paris Saclay, CEA,
CNRS, 91191 Gif-sur-Yvette, France
21
Laboratoire APC, Paris, France
22
LISA NL Group, RU physics, Netherland
23
IUCAA
24
IRFU Saclay, France
25
Portsmouth University, UK
26
Department of Mathematics and Statistics, University of Otago,
New Zealand
27
CEICO - Czech Academy of Sciences, Prague, Czechia
28
Van Swinderen Institute for Particle Physics and Gravity,
University of Groningen, the Netherlands
29
SYRTE, Observatoire de Paris, France
30
Theoretical Particle Physics and C osmology Group, Physi cs
Department, King’s College London, University of London,
Strand, London WC 2R 2LS, UK
31
University College London, UK
32
LISA NL Group, University of Twente, Netherland
33
Theoretical Physics Group and Quantum Alberta, Department
of Physics and As tr onomy, University of Lethbridge, 4401 Univer-
sity Drive, Lethbridge, Alberta T1K 3M4, Canada
34
Departments of As tr onomy and Physics, University of Arizona,
Tucson, Arizona 85721, USA
35
Johannes Gutenberg University Mainz, Institute for Physics,
Germany
36
LISA NL Group, Nikhef, Netherland
37
University of Edinburgh, UK
38
GGC Gravity Group
39
Instituto de Estructura de la Materia - CSIC, Madrid, Spain
40
Institute for Theoretical Physics, Univer sity of Amsterdam, PO
Box 94485, 1090GL Amsterdam
41
Universita L’Aquila, Italy
42
Department of Physics, U niversity of Illinois at Urbana-
Champaign, Urbana, IL 61820, USA
43
Jet Propulsion Laboratory, Caltech, USA
44
Cornell, USA
45
Kepler Center T¨ubingen (KeCeT), Germany
46
Universit´e Libre de Bruxelles, CP 231, B-1050 Brussels, Belgium
47
Uppsala University, Sweden
48
Imperial College London, UK
49
Instituto Superior Tecnico, Portugal
50
Case Western Reserve University, USA
51
University of Sheffield, UK
52
NZ Astrostatistics and GR, University of Auckland, New-
Zealand
53
Cardiff University Gravity Exploration Institute, UK
54
Wilbur Wright College, Chicago, USA
55
Institute of Cosmology and Gravitation, University of
Portsmouth, UK
56
MSLU, Russ ia
57
Japanese working group for LISA science, YITP, Kyoto Univer-
sity
58
Taiwan Consortium for Gravitational Wave Research, National
Tsing Hua University, Taiwan
59
Szeged Gravity Group, University of Szeged, Hungary
60
School of Physics and Astronomy and Institute for Gravitational
Wave Astronomy, University of Birmingham, Birmingham, B15
2TT, UK
61
Haggard Research Group at McGill University
62
Taiwan Consortium for Gravitational Wave Research, Academia
Sinica, Taiwan
63
Shanghai Astronomical Observatory, CAS, China
64
Aix Mar seille Univ, CNRS/IN2P3, CPPM, Marseille, France
65
Glasgow LISA Science, UK
66
University of Stavanger, Norway
67
Humboldt State University Gravitational R esearch Laboratory
68
LIGO Laboratory, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139, USA
69
CENTRA, Departamento de Fisica, Instituto Superior T´ecnico
- IST, Univers idade de Lisboa - UL, Avenida Rovisco Pais 1,
3
1049-001 Lisboa, Portugal
70
University of California, Davis, USA
71
Cornell University, USA
72
Lohrmann Observatory, Technische Universit??t Dresden,
Germany
73
University of Wisconsin - Madison, USA
74
Massachusetts Institute of Technology, USA
75
Taiwan Consortium for Gravitational Wave Research, National
Taiwan Normal University, Taiwan
76
Taiwan Consortium for Gravitational Wave Research, Tamkang
University, Taiwan
77
CSU Fullerton Gravitational-Wave Physics and Astronomy
Center, USA
78
University Granada, Spain
79
eXtreme Gravity Institute, Montana State University, USA
80
Complutense U niversity of Madrid & IPARCOS, Spain
81
Japanese working group for LISA science, Ryukoku University
82
Technical University of Liberec, Czech Republic
83
Department of Physics, Aristotle University of Thessaloniki,
Thessaloniki, Greece
84
CAUP and IA-Porto, Portugal
85
Harvard-Smi thsonian Center for Astrophysics, USA
86
LISA NL Group, UU physics, Netherland
87
Harvard Physics, USA
88
NCSA, University of Illinois at Urbana-Champaign Department
of Physics, USA
89
ISS-Sci, R omania
90
Japanese working group for LISA science, Kyushu University
91
Kavli Institute for Astronomy and Astrophysics, Peking Univer-
sity, Beijing 100871, China
92
Georgia Tech, USA
93
Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer
de Can Magrans s /n, 08193 Cerdanyola del Vall`es (Barcelona),
and Institute of Space Studies of Catalonia (IEEC), Carrer del
Gran Capit`a, 2-4, Edifici Nexus, despatx 201, 08034 Barcelona,
Spain
95
Universit´e d’Orl´eans CNRS (LPC2E), France
96
Japanese working group for LISA science, ICRR, University
Tokyo
97
Japan instrument group, Japan
98
Japanese working group for LISA science, Kyoto University
99
APC and Institut d’Astrophysique de Paris, CNRS and Sor-
bonne Universit´es, UMR 7095, 98 bis bd Ar ago, 75014 Paris,
France
100
University of Minnesota / CEICO, USA
101
Tata Institute of Fundamental Research, Homi Bhabha Road,
Mumbai 400005, India
102
Kyoto University, Japan
103
UFL: LISA group at University of Florida, USA
104
NZ Astrostatistics and GR, University of Canterbury, New-
Zealand
106
University of Texas at Austin, USA
107
UC Berkeley, USA & IPhT Saclay, France
108
Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma
de Madrid, Cantoblanco 28049 Madrid, Spain
109
Laboratoire de Physique et Chimie de l’Environnement et de
l’Espace LPC2E UMR7328, Universit´e d’Orl´eans, CNRS, F-45071
Orl´eans, France
110
Center for Particle Cosmology, Department of Physics and
Astronomy, University of Pennsylvania, 209 S. 33rd St., Philadel-
phia, PA 19104, USA
111
TRIUMF, Canada
112
Van Swinderen Institute, U niversity of Groningen, 9747 AG,
Groningen, Netherlands
113
University of Chinese Academy of Sciences (UCAS)
114
Kavli Institute for Cosmological Physics, The University of
Chicago, USA
115
ESOC - European Space Operations Centre, D-64293 Darm-
stadt, Germany
116
Max Planck Institute for Gravitational Physics, Potsdam,
Germany
117
SISSA, International School for A dvanced Studies, Via
Bonomea 265, 34136 Trieste, Italy
118
Laboratoire Astroparticule et Cosmologie, CNR S, Universit´e
Paris Diderot, 75013, France
119
School of Physics and Astronomy and Institute for Gravita-
tional Wave Astronomy, University of Birmingham, Birmingham,
B15 2TT, UK
120
CIDMA and Aveiro University, Portugal
121
Victoria University of Wellington, New Zealand
122
Physics Department, Technion, 3200003 Haifa, Israel
123
Center for Computational Astrophysics, Flatiron Institute, 162
5th Ave, New York, NY 10010
124
Department of Physics, University of California, Santa Barbara,
CA 93106
125
Institute for Theoretical Physics, KU Leuven, Celestijnenlaan
200D, B-3001 Leuven, Belgium
126
School of Physics and Astronomy, University of Nottingham,
Nottingham, NG7 2RD, UK
127
Theoretical Physics Department, CERN, 1 Esplanade des
Particules, CH-1211 Geneva 23, Switzerland
128
INFN, Sezione di Padova, via Marzolo 8, I-35131, Padova, Italy
129
Department of Applied Mathematics, The University of
Western Ontario, N6A 5B7, London, Ontario, Canada
130
Swansea Univer sity, U K
131
Theoretical Physics Group, Department of Physics, Kuwait
University, P.O. Box 5969, Safat 13060, Kuwait
132
IA, Portugal
In this paper, which is of programmatic rather than
quantitative nature, we aim to further de line ate and
sharpen the future potential of the LISA mission in the
area o f fundamental physics. Given the very broad range
of topics that might be relevant to LISA, we present here
a sample of what we view as particularly promising fun-
damental physics directions. We organize these direc-
tions through a “science-first” approach that allows us
to classify how L I SA data can inform theoretical physics
in a variety of areas. For each of these theoretical phy sics
classes, we identify the sources that ar e curr ently ex-
pected to provide the principal contribution to our knowl-
edge, and the areas that ne ed further development. The
classification presented here should not be thought of as
cast in stone, but rather as a fluid framework that is
amenable to change with the flow of new insights in the-
oretical physics.
4
I. INTRODUCTION
Several of the deepest open questions in fundamental
physics involve gravity in one way or another. These in-
clude the classical and quantum dynamics of black holes,
a detailed under standing of the expansion and structure
formation history in cosmology, and of cours e the funda-
mental nature of gravity and spacetime itself.
Gravitational wave (GW) observations have an enor-
mous potential to inform and to falsify theoretical work in
these areas, leading to exciting prospects for a fruitful in-
terplay between fundamental theory and observation. On
the one hand GWs give us access to largely unexplored
regions of the universe that are dark, such as the imme-
diate environment of black holes and the earliest phases
of large-scale structure formation, and to regions whe re
light cannot penetrate, such as the very early universe.
On the other hand GWs provide a source of informa-
tion that complements conventional astronomy and cos-
mology, enabling a “multi-messenger” approach, thereby
paving the way for a deeper understanding.
The observation of long-wavelength GWs with LISA
[
1] is particularly promising as a probe of fundamenta l
physics. Potential examples are anomalies in the data
related to gravitational parity violation, which could pro-
vide a hint toward a resolutio n of the baryogenesis pro b-
lem. Other anomalies related to violations of the Equiva-
lence Principle or Lorentz invariance could produce mod-
ifications in the dispersion relation of matter or horizon-
scale modifications in black hole physics due to quantum
gravity effects. Observations of the dispe rsion relation of
GWs could constrain a large class of modified theories,
which include massive gravity models tha t attempt to ex-
plain the late-time acceleration of the universe, as well as
other Lorentz-violating theories (such as Eins tein-æther
or Horava gr avity), whose renormalizability makes them
attractive candidates for quantum gravity.
The observational input that LISA will provide will
also be complementary to that following from ground-
based GW observations [
2–4], carried out by LIGO,
VIRGO and KAGRA, because the target sources are
qualitatively different. LI SA w ill observe GWs at much
lower frequencies than ground-based instruments, allow-
ing for the measurement of an entirely different clas s of
sources: supermassive black hole mergers, E MRIs, galac-
tic binaries, and stochastic GW backgrounds. Some of
these sources, such as supermassive black hole mergers,
will lead to extremely loud signals, with signal-to-noise
ratios in the thousands, that will allow for a deep s earch
of anomalies. Other classes of sources will lea d to signals
that may not be very loud, such as the EMRIs, but that
will nonetheless be extremely complex with lots of am-
plitude and phase modulations, allowing for the search
of qualitatively different anomalies. Moreover, weak sig-
nals may allow for tests of General Relativity (GR) that
are statistically enha nc e d by the large number of events,
and which might therefore be comp e titive against single
events with extre mely larg e s ignal-to-noise ratios. LISA
observations also c omplement future GW observations
via pulsar timing arrays and the B-mode polarization in
the cosmic microwave back ground, both of which probe
an even lower GW frequency range.
The goal of this paper is to identify and scientifically
motivate a sample of topics in fundamental physics be-
yond the current standar d models of particle physics,
gravity a nd cosmology that we view are particularly rele-
vant for the LISA scientific community. These topics are
of interest to several Working Groups (WG) organized
within the LISA Consortium: the Fundamental Physics,
the Cosmology, the Astrophysics, and the Waveform-
Modeling WGs, each of which approaches these from a
different, complementary angle. We stress that here we
shall discuss all the topics in a qualitative way, as pre-
cisely the more quantitative aspects will be subject to de-
tailed investigations and are thus as such not yet know.
Once new results will be available the relevance of cer-
tain topics will of course change and new ones, not yet
known, might arise. Thus this paper has to be seen as
a first step with the aim to somehow coordinate the ef-
fort needed towards formulating a realistic assessment in
the area of the fundamental physics fea sible with LISA.
Thus this paper will definitively rise more questions than
giving answers.
This initia tive should be viewed not as an exhaustive
classification but rather as a warmup for a more compre-
hensive and detailed account in the future. Our discus-
sion will be organized in a science-first approach. That
is, instead of first thinking about so urces of GWs, we
will first think about the theoretical physics that could
be learned with LISA, irrespective of the source class.
Of course, any s uch list will be, by definition, incom-
plete, and p erhaps more importantly, only a snapshot
of the interests of the field at the time of writing. One
should thus think of the classes we will identify below
as fluid, subject to change in the future, as the winds of
physics start blowing in a different direction. With this
caveat in mind, we identify the science drivers presented
in Fig.
1, with each scie nc e driver defined and discussed
in much more detail in each of the sections that follows.
This classification implicitly assumes that work must be
done in three main areas : theoretical development, wave-
form generation, and data analysis, with different drivers
currently at different levels of development.
With the classes declared, we will then sub-organize
each class with s ub-classes, following a source classifica-
tion approa ch. For the purpose of this document we will
identify six differe nt s ource sub-classes :
• Supermassive Black Hole Binaries (SMBHBs): Co-
alescences with mass ratio larger than 10
−1
and
total masses in (10
5
, 10
7
)M
⊙
.
• Intermediate-Mass Black Hole Binaries (IMBHBs):
Coalescences with mass ratio larger than 1 0
−1
and
total masses in (10
2
, 10
5
)M
⊙
.
• Extreme mass-ratio and intermediate mass-ratio
inspirals (EMRIs and IMRIs): Coalescences with
5
FIG. 1. A taxonomy of LISA-related topics in fundamental
physics. Each of them is discussed in a separate section in this
paper. The ellipses stand for topics that may be considered
in the future.
mass ratios in (10
−6
, 10
−3
) and (10
−3
, 10
−1
), and
total masses in (10
3
, 10
7
)M
⊙
.
• Stellar origin BH binaries (SOBHBs): Inspi-
rals with sufficiently low total mass (e.g. in
(50, 500)M
⊙
) such that they could be detected both
by LISA and second- or thir d-generation ground-
based detectors.
• Galactic Binaries: White dwarf or neutron sta r bi-
nary ins pirals within the Milky Way that produce
nearly monochromatic signals.
• Stochastic Backgrounds: Cosmological sources of
GWs that produce a stochastic background.
Of these source sub-classes, SMBHBs with accretion
disks, SOBHBs in nuclear galactic disks [
5], and galac-
tic binaries are expected to produce strong and coinci-
dent electromagnetic signals. By no means ought this
to be thoug ht of as final, since LISA could alway s de-
tect sources that nobody expected. Inversely, we make
no statements in this document about the astrophysical
rates of these events, or even whether all of these will be
detectable with LISA, as this will depend on the noise of
the actual detector (see e.g. [
6]).
The rest of this paper is organized as follows. Section II
discusses modified dis persion relations and the speed of
gravity. Sec tion I II describes violatio ns of the Equiva-
lence Principle and violations of other fundamental sym-
metries. Section
IV covers tests of the nature of black
holes. Section
V discusses dark energy and screening.
Section
VI describes dark matter and primordial black
holes. Section
VII s umma rizes ideas for other model-
independent tests. Section VIII discuss e s a strophysical
systematics, while Sec.
IX covers waveform systematics.
Section X summarize s and concludes w ith an outlook to
the future. Henceforth, we employ geometric units when
needed, in which G = 1 = c and we follow the conven-
tions of [
7].
II. MODIFIED DISPERSION RELATIONS AND
THE SPEED OF GRAVITY
According to Einstein’s theory, GWs obey the disper-
sion relation ω
2
= k
i
k
i
, with the contraction done with
the flat Euclidean metric. This then immediately implies
that the group and the phase velocity of GWs are the
speed of light. Modified theories of gravity, in particu-
lar those that attempt to unify quantum mechanics and
GR, sometimes lead to different dispersion re lations of
the fo rm
ω
2
= k
i
k
i
+
m
2
g
~
2
+ A(k
i
k
i
)
α
, (1)
where m
g
is a hypothetical mass for the graviton, α ∈
R\{0} determines the type of modification introduced,
and A controls its magnitude. This expression should be
thought of as approximate, in the limit that m
2
g
/~
2
≪ k
2
and A ≪ k
2−α
.
The parameteriz ation of the correction to the propaga -
tion of GWs presented in Eq. (
1) is obviously not unique,
and other parameterizations have been considered in the
literature, especially in the context of cosmology [
8–11].
A commonly used parameterization is
ω
2
+ iHω (3 + α
M
) = (1 + α
T
) k
i
k
i
, (2)
where we are here considering waves propagating in a
cosmological background with Hubble parameter H. A
more detaile d discussion on these assumptions and con-
sequences for bla ck-hole properties can be fo und in [12].
Clearly, α
T
= A when α = 1, and it controls the
speed of GWs. The parameter α
M
is not included in
Eq. (
1), and it co ntrols the rate of dissipation of GWs
(see e.g. [
13]). Both parameter izations have advantages
and disadvantages. For example, Eq. (1) allows one to
constrain a kinematical graviton mass, while Eq. (
2) does
not, whereas Eq. (2) allows one to test the rate of GW
dissipation, while Eq. (
1) does not.
A modification of this type cle arly leaves an imprint
on the GWs that arrive on Earth, but this imprint is due
to modifications in the propagation of the waves, and not
modifications in their generation. One can think of this
modification as a correction to the graviton propagator
in quantum field theory language. Given this, one can in
principle modify any wave generation scheme by simply
modifying the way the GWs propagate from the source
to the detector on Earth in vacuum. Fo r a more detailed
review of the way this modification affects the response
function, see [
14, 15].
The bes t systems to constrain these modifications a re
those that are as far away as possible from Earth, which
