ELGAR—a European Laboratory for Gravitation and Atom-interferometric Research [original]

Classical and Quantum Gravity

Class. Quantum Grav. 37 (2020) 225017 (35pp) https://doi.org/10.1088/1361-6382/aba80e

ELGAR—a European Laboratory for

Gravitation and Atom-interferometric

Research

BCanuel

1,∗,SAbend

2, P Amaro-Seoane3,4,5,6,

F Badaracco7,8, Q Beaufils9, A Bertoldi1, K Bongs10,

PBouyer

1,CBraxmaier

11,12,WChaibi

13, N Christensen13,

FFitzek

2,14, G Flouris15, N Gaaloul2,SGaffet

16,

C L Garrido Alzar9,RGeiger

9, S Guellati-Khelifa17,

K Hammerer14,JHarms

7,8, J Hinderer18, M Holynski10,

J Junca1, S Katsanevas19,CKlempt

2,CKozanitis

15,

MKrutzik

20, A Landragin9,IL

azaro Roche16,

B Leykauf20 ,Y-HLien

10, S Loriani2,SMerlet

M Merzougui13,MNofrarias

21,22 , P Papadakos15,23 ,

F Pereira dos Santos9,APeters

20 , D Plexousakis15,23,

MPrevedelli

24 , E M Rasel2, Y Rogister18, S Rosat18 ,

A Roura25 , D O Sabulsky1, V Schkolnik20,

D Schlippert2, C Schubert2,31, L Sidorenkov9,

J-N Siemß2,14 , C F Sopuerta21,22 ,FSorrentino

26,

C Struckmann2,GMTino

27 , G Tsagkatakis15,23,

A Vicer´

e28,29 , W von Klitzing30 ,LWoerner

11,12 and

X Zou1

1Univ. Bordeaux, CNRS, IOGS, LP2N, UMR 5298,F-33400 Talence, France

2Leibniz Universit¨

at Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167

Hannover, Germany

3Universitat Polit`

ecnica de Val`

encia, IGIC, Spain

4Kavli Institute for Astronomy and Astrophysics, Beijing 100871, China

5Institute of Applied Mathematics, Academy of Mathematics and Systems Science,

CAS, Beijing 100190, People’s Republic of China

6Zentrum für Astronomie und Astrophysik, TU Berlin, Hardenbergstraße 36, 10623

Berlin, Germany

7Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy

8INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy

9SYRTE, Observatoire de Paris, Universit´

e PSL, CNRS, Sorbonne Universit´

e, LNE,

61 avenue de l’Observatoire, 75014 Paris, France

31Current address: German Aerospace Center (DLR), Institute for Satellite Geodesy and Inertial Sensing, c/o Leibniz

Universit¨

at Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany.

∗Author to whom any correspondence should be addressed.

Original content from this work may be used under the terms of the Creative Commons

Attribution 4.0 licence. Any further distribution of this work must maintain attribution

to the author(s) and the title of the work, journal citation and DOI.

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

10 Midlands Ultracold Atom Research Centre, School of Physics and Astronomy,

University of Birmingham, Birmingham, B15 2TT, United Kingdom

11 ZARM, Unversity of Bremen, Am Fallturm 2, 28359 Bremen, Germany

12 DLR, German Aerospace Center, Linzer Strasse 1, 28359 Bremen, Germany

13 ARTEMIS, Universit´

e Côte d’Azur, Observatoire de la Côte d’Azur, CNRS,

F-06304 Nice, France

14 Institute for Theoretical Physics and Institute for Gravitational Physics

(Albert-Einstein-Institute), Leibniz University Hannover, Appelstrasse 2, 30167

Hannover, Germany

15 Institute of Computer Science, Foundation for Research and Technology—Hellas,

70013, Heraklion, Greece

16 LSBB, Laboratoire Souterrain Bas Bruit, CNRS, Avignon University—La grande

combe, 84400 Rustrel, France

17 Laboratoire Kastler Brossel, Sorbonne Universit´

e, CNRS, ENS-PSL Research

University, Coll`

ege de France, 4 place Jussieu, 75005 Paris, France

18 Institut de Physique du Globe de Strasbourg, UMR 7516, Universit´

ede

Strasbourg/EOST, CNRS, 5 rue Descartes, 67084 Strasbourg, France

19 European Gravitational Observatory (EGO), I-56021 Cascina (Pi), Italy

20 Humboldt-Universit¨

at zu Berlin, Institut für Physik, Newtonstraße 15, 12489

Berlin, Germany

21 Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans

s/n, 08193 Cerdanyola del Vall`

es (Barcelona), Spain

22 Institute of Space Studies of Catalonia (IEEC), Carrer del Gran Capit`

a, 2-4,

Edifici Nexus, despatx 201, 08034 Barcelona, Spain

23 Computer Science Department, University of Crete, 70013, Heraklion, Greece

24 Dept. of Physics and Astronomy, Univ. of Bologna, Via Berti-Pichat 6/2, I-40126

Bologna, Italy

25 Institute of Quantum Technologies, German Aerospace Center (DLR), Söflinger

Str. 100, 89077 Ulm, Germany

26 Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Genova, via Dodecaneso

33, Genova, Italy

27 Dipartimento di Fisica e Astronomia and LENS Laboratory, Universit`

a di Firenze

and INFN-Sezione di Firenze, via Sansone 1, Sesto Fiorentino, Italy

28 Universit`

a degli Studi di Urbino ‘Carlo Bo’, I-61029 Urbino, Italy

29 INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy

30 Institute of Electronic Structure and Laser, Foundation for Research and

Technology - Hellas, 70013, Heraklion, Greece

E-mail: benjamin.canuel@institutoptique.fr

Received 21 February 2020, revised 9 July 2020

Accepted for publication 21 July 2020

Published 28 October 2020

Abstract

Gravitational waves (GWs) were observed for the first time in 2015, one cen-

tury after Einstein predicted their existence. There is now growing interest to

extend the detection bandwidth to low frequency. The scientific potential of

multi-frequency GW astronomy is enormous as it would enable to obtain a

more complete picture of cosmic events and mechanisms. This is a unique

and entirely new opportunity for the future of astronomy, the success of which

depends upon the decisions being made on existing and new infrastructures.

The prospect of combining observations from the future space-based instrument

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

LISA together with third generation ground based detectors will open the way

toward multi-band GW astronomy, but will leave the infrasound (0.1–10 Hz)

band uncovered. GW detectors based on matter wave interferometry promise

to fill such a sensitivity gap. We propose the European Laboratory for Grav-

itation and Atom-interferometric Research (ELGAR), an underground infras-

tructure based on the latest progress in atomic physics, to study space–time

and gravitation with the primary goal of detecting GWs in the infrasound band.

ELGAR will directly inherit from large research facilities now being built in

Europe for the study of large scale atom interferometry and will drive new

pan-Europeansynergies from top research centers developing quantum sensors.

ELGAR will measure GW radiation in the infrasound band with a peak strain

sensitivity of 3.3×10−22/√Hz at 1.7 Hz. The antenna will have an impact

on diverse fundamental and applied research fields beyond GW astronomy,

including gravitation, general relativity, and geology.

Keywords: gravity, gravitational waves, research infrastructure, cold atoms,

matter-wave interferometry

(Some figures may appear in colour only in the online journal)

Introduction

The first confirmed observation of gravitational waves (GWs) [1] opened a new window into

the study of the Universe by accessing signals and revealing events hidden to standard obser-

vatories, i.e. electromagnetic [2] and neutrino [3] detectors. Since then, several violent cosmo-

logical events have been reported, in detail ten binary black hole (BH) mergers and a binary

neutron star (BNS) inspiral [4]. Moreover, the complimentary information provided by GW

astronomy could, for example, bring new insight for the study of dark matter (DM) or the

exploration of the early Universe, where light propagation was impossible. Expected sources

of GWs range from well understood phenomena, such as the merging of neutron stars or BHs

[5], to more speculative ones, such as cosmic strings [6] or early Universe phase transitions

[7].

The era of GW astronomy was opened by the ‘second’ generation of laser interferometers

LIGO [8]andVIRGO[9] that operate in a frequencyband ranging from 10 Hz to 10 kHz. Other

instruments operating in different frequency ranges are now required to expand the breadth of

GW astronomy. Exploring the Universe with GWs from low to high frequencies (mHz to kHz)

can render possible the discovery of new sources of GWs. This is a unique opportunity to

expand our knowledge of the laws of nature, cosmology, and astrophysics [10]. The success of

future GW astronomy depends on the choice of low frequency GW detectors. The proposal to

construct the space-based Laser Interferometer Space Antenna (LISA) [11] to investigate GWs

sources at very low frequency, combined with the planned third generation ground-based laser

interferometer (Einstein Telescope—ET) [12] will contribute to ‘multiband GW astronomy’,

but will leave the infrasound (0.1–10 Hz) band uncovered. An infrasound GW detector is crit-

ical to the completion of available and considered observation windows in GW astronomy [5,

13–15]; such instrument could help answer long-standing questions of cosmology involving

dark energy, the equivalence principle, cosmic inflation, and the grand unified theory.

The European Laboratory for Gravitation and Atom-interferometric Research (ELGAR)

proposes matter-wave interferometry to fill the sensitivity gap in this mid-band. One cen-

tury after the discovery of quantum mechanics and general relativity, advanced concepts have

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

resulted in dramatic progress in our ability to control matter at the quantum level. Manipulating

atoms at a level of coherence that allows for precise measurement has led to the development

of extremely sensitive inertial sensing devices that measure, with high accuracy and precision,

accelerations [16,17], rotations [18–20], and even the tidal force induced by the spacetime

curvature [21]. The outstanding performances of inertial atom sensors motivate the surge of

atom interferometer (AI) experiments both in fundamental physics—e.g., to measure funda-

mental constants [22,23], test general relativity [24–29], and set limits on dark energy forces

[30–32]—and in applied contexts [33]—e.g., space geodesy [34], geophysics [35–37], and

inertial navigation [38,39]. Triggered by the latest progress in this field, ELGAR will use a

large scale, multidimensional array of correlated AIs in free fall [40]. In such a scheme, the

GW signal is obtained by an a set of differential measurements between the different matter

wave interferometers, providing a strong immunity to seismic noise and an important rejection

of Newtonian noise (NN), i.e. two of the most important effects impacting the performances

of infrasound GW detectors.

The future infrastructure will not only fill the gap of infrasound GW observation, but could

also have applications in other research domains including fundamental physics, gravitation,

general relativity, and geology. ELGAR will monitor the evolution of Earth’s gravitationalfield

and rotation rate in three dimensions, thus improving our understanding of geophysical fluctu-

ations of Earth’s local gravitational field, as well as our knowledge of slow variations in gravity

gradients and rotations. The data produced by ELGAR could allow empirical tests of funda-

mental theories of physics with unprecedented precision. For example, precise time-mapping

of the fluctuation of gravitational forces could provide limits on the violations of Lorentz invari-

ance [41] and an improved understanding of gravitational quantum mechanics [42–45]. The

precise monitoring of Earth’s rotation could also shed light on the Lense–Thirring effect [46],

one of the many effects predicted by general relativity [24].

This paper is organized as follows: section 1first introduces the measurement concept of

large-scale atom interferometry. It then details the ELGAR geometry, derives its sensitivity to

GWs and noise sources, and finally presents its main technological bricks. Section 2presents

the operating parameters and the sensitivity curve of the antenna and discuss its complementary

with other GW detector projects. Section 3then studies the new possibilities offered by ELGAR

for astrophysics, gravity and fundamental physics.

1. Detector configuration and signal extraction

1.1. Atom interferometry

An AI utilizes matter-wave beam splitters and mirrors to create a quantum mechanical analog to

an optical interferometer [47]. Atom interferometric techniques take advantage of a fundamen-

tal property of quantum mechanics, interference, to offer unparalleled sensitivity to changes in

space–time. Here, we briefly introduce atom interferometry before delving into more details

in later sections.

The atomic wave-function needs to be split, deflected, and recombined in order to observe

interference, just like an electromagnetic wave in an optical interferometer. After splitting,

the atomic wave-packet follows a superposition of two different paths and the interference

pattern obtained after its recombination is a function of the relative phase shift accumulated

along the paths. This phase shift is the result of free evolution of the atomic wave-function

along each path [48]. We focus our attention on light pulse AIs, where the interrogation of the

atoms for splitting, deflecting, and recombining is accomplished using coherent pulses of laser

light [49]. The space–time diagram in figure 1showsaschematicversionofthisprocessfora

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 1. Space–time diagram schematic of an AI using light pulses. The atomic tra-

jectories are represented in black: the solid lines refer to the propagation in state |1,

the dashed ones in state |2. The propagation paths are represented as straight lines,

whereas uniform gravity makes them parabolic. The two states have a momentum sep-

aration given by the two-photon momentum exchange imparted by the interferometric

pulses, represented by the sinusoidal red lines.

single atom. An AI of this type measures the motion of the atomic wave-function relative to the

reference frame defined by the laser phase fronts. This has made light pulse atom interferometry

a platform for inertial sensors that offers unparalleled precision and accuracy [50]. Sensitivity

to GWs is intrinsically linked to the response of an AI to the local phase of the manipulating

optical field: the GW induces a variation of the travel time of photons between the atom and

the laser [51].

The measurement of the AI phase requires a number of steps including preparation of

the atomic sample, coherent manipulation of the matter waves which defines the instrument

geometry and sensitivity, and finally detection of the output ports. Restricting our discus-

sion to AIs using cold atom in free-fall [49], sample preparation requires collecting a dilute

cloud of cold atoms, prepared with standard laser cooling and trapping techniques [52]. Using

ensembles with a small spread of momenta around their center-of-mass velocity ensures that

atoms travel along the intended trajectory and avoids introducing spurious signals or reduc-

ing the interferometric contrast. After the cooling phase, these ensembles are transferred into

the interferometer region by launching them onto a ballistic trajectory, accomplished via a

moving molasses [53], coherent momentum transfer from laser light [54,55], or by simply

dropping them. This transfer allows for the separation of the interferometric region from the

atomic source, and in turn to optimize several parameters like vacuum pressure and optical

access, independently. In the interferometer zone, a sequence of light pulses is applied to

the atomic ensemble, to coherently divide, deflect, and finally recombine the wave-functions.

The light pulses are functionally made into beam splitters or mirrors based on the amount

of time in which they shine the atomic ensembles. While illuminating the atoms, the res-

onant electromagnetic field introduces coherent transitions between different atomic states,

so-called Rabi oscillations. A beam splitter is realized for the pulse time corresponding to

the creation of a superposition of states with equal probability, obtained at a fourth of a Rabi

period and thus called a π/2 pulse. In a similar way, a πpulse corresponds to a flipping

of the atom states and to the realization of a mirror for the matter-waves. The interrogation

sequence—defining the succession of πand π/2 pulses and their distance in time—together

with the direction of light with respect to the atom trajectory will define the sensitivity of

the AI.

We now focus on techniques suitable to the ELGAR project. The antenna uses various

laser cooling techniques for an all-optical production of atom ensembles with a 3D kinetic

temperature below 1 μK, while maintaining a density dilute enough to mitigate atom–atom

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 2. Example schematic of a four-pulse AI. (a) Horizontal setup. A cloud with

some initial momentum is interrogated by a lower beam tuned to implement a π/2 pulse

while an upper beam, where the apogee is, operates as a πpulse. The atoms begin to

fall with gravity and they are recombined with another π/2 pulse when they fall through

lower interrogation beam. After, the population imbalance is measured which is a direct

measurement of the atomic phase. (b) Vertical setup. The same interferometer geometry,

under constant gravitational acceleration.

interactions—see section 1.4.3 and [56]. After cooling, atoms are launched on a vertical

parabolic trajectory into the interrogation region, where the interferometer is created in a sym-

metric way around the apogee using a set of two horizontal laser beam—see figure 2(a).

Different interferometer sequences can be used for ELGAR; we focus our attention on the

four-pulse ‘butterfly’ [57] configuration, whose geometry is shown in figure 2, which con-

sists of a sequence of π/2–π–π–π/2 pulses separated in time by T–2T–T. This configuration

[58], first proposed to measure gravity gradients, shows no sensitivity to DC accelerations and

offers robustness against spurious phase terms. The first interferometer pulse is a beam split-

ter, putting the atomic ensemble into a superposition of states. The second and third pulses

deflect the states, and create a folded geometry. At the location of the second beamsplitter,

the trajectories overlap and the two output ports are measured. The details of the interrogation

process can be found in section 1.4.2 and [56]. In brief, among the multiple techniques for the

exchange of momentum between atoms and photons, the ELGAR project will focus on Bragg

diffraction and Bloch oscillations [59], based on their scalability and demonstrated efficacy

[60] in highly sensitive AI setups. At the conclusion of the interferometer, each atom of the

ensemble is in a superposition of the output states. For detection, we measure one observable

of this quantum system, the occupancy of the states. This operation is typically accomplished

using a variety of destructive readout techniques, such as fluorescence and absorption [61],

to obtain the probability that an atom will be found in a particular state. This probability is a

function of the relative phase acquired along the paths of the interferometer, which depends

upon the variation of the interrogation laser phase during the time of the interferometer, where

such variations may arise from the effect of incident GWs.

Based on the horizontal interferometer geometry presented here, we now consider the sen-

sitivity to GWs obtained from a gradiometric configuration using two spatially separated AIs,

the basis of the ELGAR detector.

1.2. GW signal from an atom gradiometer

Here we present a schematic description of how the ELGAR detector is sensitive to GWs.

As shown in figure 3, we consider an atom gradiometer using two free-falling AIs placed at

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 3. Gravity gradiometer schematic diagram. Two AIs placed at Xi,jare separated

by a distance Land coherently manipulated by a common laser retro-reflected by a mirror

placed at position MX. Adapted from [67].

positions Xi,jalong the x-axis and interrogatedby a common laser beam which is retro-reflected

by a mirror placed at position MX. The geometry of each AI is the four-pulse (π/2–π–π–π/2)

presented in the previous section. The interferometric signal is read out as a ground state

population imbalance that depends upon the phase difference Δϕlas between the two counter-

propagating beams. Considering large momentum transfer (LMT) techniques where 2npho-

tons are coherently exchanged during the interrogation process, the output phase Δφ(Xi,t)of

the AI at position Xiand time tis:

Δφ(Xi,t)=n∞

−∞

Δϕlas(Xi,τ)g(τ−t)dτ+(Xi,t), (1)

where gis the time derivative of the sensitivity function of the AI [62,63]and(Xi,t)is

the detection noise related to the projection of the atomic wave-function during the mea-

surement process. Accounting for the effects of laser frequency noise δν(τ), vibration of the

retro-reflecting mirror δxMX(τ), GW strain variation h(τ), and fluctuation of the mean trajec-

tory of the atoms along the laser beam direction induced by the fluctuating local gravity field

δxat(Xi,τ), the last equation can be written as [40,64]:

Δφ(Xi,t)=∞

−∞

2nklδν(τ)

ν+h(τ)

2(MX−Xi)

+δxMX(τ)−MX−Xi

cδx

MX(τ)−δxat(Xi,τ)g(τ−t)dτ+(Xi,t), (2)

where kl=2πν

cis the wave number of the interrogation laser. It should be noted that seismic

condition does not only impact movement of the retro-reflector, linked to the term [δxMX(τ)−

MX−Xi

cδx

MX(τ)], but also creates frequency noise from movement of the input optics, which is

included in the term δν(τ)

ν. By simultaneously interrogating two AIs with the same laser, one

can cancel the sensitivity to position of the retro-reflecting mirror, a common-mode noise. The

resulting differential phase ψ(Xi,Xj,t)is[64]:

ψ(Xi,Xj,t)=Δφ(Xi,t)−Δφ(Xj,t)=∞

−∞

2nklδν(τ)

ν+h(τ)

2−δx

cL

+δxat(Xj,τ)−δxat(Xi,τ)g(τ−t)dτ+(Xi,t)−(Xj,t).(3)

With the assumption that the detection noise is spatially uncorrelated, we write the power

spectral density (PSD) of the differential interferometric phase as:

Sψ(ω)=(2nkl)2Sδν(ω)

ν2+Sh(ω)

4+ω2

c2SδxMX(ω)L2+SNN1(ω)|ωG(ω)|2

+2S(ω), (4)

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

where Sudenotes the PSD of a given time function u(t). The term G(ω) represents the Fourier

transform of the sensitivity function of the interferometer to phase variations, which for the

four-pulse configuration is [63]:

|ωG(ω)|2=64 sin2(ωT)sin

4ωT

2,(5)

In equation (4)thetermSNN1(ω) is the PSD of the relative displacement of the atom test masses

with respect to the interrogation laser:

NN1(t)=δxat(Xj,t)−δxat(Xi,t), (6)

which is related to the difference of the local gravity field between the points Xiand Xjprojected

along the gradiometer direction, so-called NN, i.e. terrestrial gravity perturbations of various

origins, which we treat in detail in [56]. This perturbation introduces an atomic phase variation

that is indistinguishable from the signal produced by an incident GW, as shown in equation (4),

and constitutes a limit for the detector that sums with other contributions.

Taking the GW term as the signal of interest in equation (4) and dividing it by the other

terms, we obtain the signal to noise ratio (SNR) of the detector. Setting the limit of detection

as an SNR of 1, we define the strain sensitivity of the gradiometer as the sum:

Sh=4Sδν(ω)

ν2+4SNN1(ω)

L2+4ω2SδxMX(ω)

c2+8S(ω)

(2nkl)2L2|ωG(ω)|2.(7)

Here, we have derived the sensitivity of an atom gradiometer to changes in space–time strain,

a configuration which is the basis of the ELGAR detector. We now present the full instrument

geometry which is configured to optimize the sensitivity to the different noise term listed in

equation (7).

1.3. The ELGAR detector

1.3.1. ELGAR structure. In order to manage the different terms limiting the strain sensitivity

of a single atom gradiometer and given in equation (7), we propose for ELGAR a detector

structure shown figure 4. The distinct feature of this geometry is the use of a 2D-array of

AIs, interrogated by a common laser beam in order to reduce sensitivity to gravity-gradient

noise. Such a noise source is expected to be one of the main limitations of the sensitivity

at low frequency of the next generation GW detectors based on optical interferometry, like

the Einstein Telescope [12]. Detectors relying on single atom gradiometers will be strongly

limited in their performances by GGN in a large portion of their sensitivity window, and it will

be crucial to mitigate its impact. To this end, we use a sensor geometry of an optimised array

to statistically average GGN [40], and bring its contribution below the target sensitivity of the

instrument.

In this geometry the laser field is divided by a beam-splitter and retro-reflected by two end

mirrors in order to obtain two symmetric and perpendicular arms in gradiometricconfiguration.

Using parameters from [40], each arm of ELGAR is composed by N=80 atom gradiometers

of baseline L=16.3 km, regularly spaced by a distance δ=200 m, leading to a total arm

length of LT=(N−1)δ+L=32.1 km.

The whole detector is placed in ultra high vacuum with a residual total pressure less than

⩽1×10−9mbar in order for gas collisions from the environment to play a marginal role

in the operation of the individual AIs. This would make the ELGAR vacuum vessel similar

in terms of size to that of existing large experiments such as VIRGO/LIGO. Such vacuum

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 4. Schematic diagram of the proposed ELGAR infrastructure. Each arm of the

detector of total length LTis formed by Ngradiometers of single baseline L. The gra-

diometers are spaced by a distance δ. The retro-reflection mirrors and the beam splitter

are placed on suspension systems. The entire detector is inside a large steel vacuum ves-

sel that maintains a base pressure of ⩽1×10−9mbar. A vertical arm could be added at

the same location or on a distributed site.

performances could be reached with a series of pumping stations distributed along the arms,

containing oil-free backing pumps and large turbo-molecular pumps but also non-evaporable

getters and ion pumps used after initial evacuation to reach high vacuum conditions. The indi-

vidual atom sources are encased inside a magnetic shield sufficient to attenuate the Earth’s

magnetic field by a factor 1000 and the interrogation region is placed in a magnetic shield

that covers the vacuum vessel in the few meters around each atom source; an example of such

system is the magnetic shielding of the MIGA demonstrator [65].

1.3.2. ELGAR GW signal extraction and strain sensitivity. To extract the GW signal, we

consider the difference between the average signals of the gradiometers of each arms:

HN(t)=HX

N(t)−HY

N(t)=1



i=1

ψ(Xi,XN+i,t)−ψ(Yi,YN+i,t).(8)

Using equation (3) we obtain:

HN(t)=1



i=1∞

−∞

2nkl−δνBs(τ)

ν+h(τ)−δx

c+δx

cL

+δxat(XN+i,τ)−δxat(Xi,τ)−δxat(YN+i,τ)+δxat(Yi,τ)g(τ−t)dτ

+(Xi,t)−(XN+i,t)−(Yi,t)+(YN+i,t).(9)

Using this differential signal cancels the contribution of common frequency fluctuations of the

interrogation laser, the only differential contribution coming from horizontal movement of the

beam-splitter that creates a frequency noise δνBs in the Y-arm of the detector:

δνBs(τ)

ν=δx

BsX

c−δx

BsY

c, (10)

where δxBsXand δxBsYare the variation of position of the beam-splitter along Xand Ydirection.

Considering that the detection noise, the end mirror and the beam-splitter displacements are

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

uncorrelated, and supposing SδxMX=SδxMY=SδxBsX=SδxBsY; we can write the PSD of the

average signal HNas:

SHN(ω)=(2nkl)2Sh(ω)+4ω2

c2SδxMX(ω)L2+SNN(ω)|ωG(ω)|2+4S(ω)

N.(11)

In this last equation, SNN is the PSD of the differential displacement introduced by the NN on

the test masses of the network NN(t), defined by:

NN(t)=1



i=1δxat(XN+i,t)−δxat(Xi,t)−δxat(YN+i,t)+δxat(Yi,t), (12)

Following the method discussed in the previous section, we obtain the strain sensitivity of the

detector exploiting the average signal as:

Sh(ω)=4ω2

c2SδxMX(ω)+SNN(ω)

L2+4S(ω)

N(2nkl)2L2|ωG(ω)|2.(13)

In comparison with the result obtained for a single gradiometer, we observe that this con-

figuration enables to mitigate the influence of the frequency noise of the interrogation laser,

while preserving sensitivity to GWs with +polarization. Evenmore, considering the average

signal also enables to partially mitigate the influence of gravity gradient noise exploiting the

space–time correlation properties of its different sources. This process is detailed in [56]: in

brief, assuming that the main sources of gravity gradient noise comes from isotropic density

fluctuations of the medium surrounding the detector linked to seismic activity and atmospheric

pressure variations, the averaging and correlation of the gradiometric phase from all partici-

pating gradiometers in the two arms enables to significantly reduce the unwanted signal from

the gravity gradient noise [40], related to the term SNN in equation (13). Indeed, in units of

strain/√Hz, this technique can reduce the contribution from GGN by a factor 1/√Nin com-

parison with the one of a single gradiometer, and can perform even better than 1/√Nif the

appropriate considerations are taken for optimizing the position of the gradiometers and the

detector site has adequate properties. For what concerns direct effect of seismic noise, related

to the term SδxMXin equation (13), this configuration has a similar sensitivity to the one of a

single gradiometer. Using a dedicated low frequency seismic attenuation system for the mir-

rors of the detector will be necessary to reduce its effects, see further details in section 1.4.4

and [56], where we evaluate in the necessary high quality isolation and suspension system,

which adopts and pushes forward key concepts devised for GW detection based on optical

interferometry.

After mitigation of the different noise sources, the sensitivity of the detector is related to

detection noise which is the last term in equation (13). This term is strongly related to the

atomic species used in the AI as well as to the transition and techniques used for detection. The

ELGAR detector can be run with different atom sources—see section 1.4.3 for a discussion

on the considered atomic species. Considering the use of 87Rb atoms launched onto a ballistic

trajectory at a flux of 1012 atoms/s, an atom shot noise limited detection, a number of photon

transferred during the interrogation of 2n=1000, and an integration time of 4T=800 ms,

this sets a detection noise limited strain sensitivity of about 4.1×10−21/√Hz at 1.7 Hz for

a single gradiometer of the network. Considering the detection noise of the 2Ngradiometers

is independent, the shot noise limited sensitivity of the whole detector goes as 1/√2Nand

improves to about 3.3×10−22/√Hz at 1.7 Hz.

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

In this section, we considered the main noise sources listed in equation (7) which are rel-

evant for the functioning principle and geometry of the detector. Other relevant backgrounds

impinging on the instrument’s sensitivity are considered exhaustively in [56]. Specifically, we

studied the coupling to the instrument signal of parameters associated to the atomic sources

(e.g. position, velocity, temperature and momentum spread of each atomic cloud), the manip-

ulation beams (e.g. their pointing jitter, and relative alignment), and the environment fluctu-

ations (e.g. gravity and its gradient, the magnetic and electric field, the blackbody radiation).

The impact of such background in terms of differential phase noise contribution are listed in

section 2.

1.4. ELGAR technologies

A detailed description of the different technological bricks for the construction of ELGAR

can be found in [56] and are summarized in the following section. We first presents different

installation sites for the infrastructure in Italy and France, which are evaluated in terms of

ambient noise. We then detail the realization of the matter wave beam splitters, the atom source

and the suspension system required for the interrogation optics of the interferometer.

1.4.1. Detector site. Candidate sites for ELGAR must meet strict environmentalrequirements,

as previous studies have shown for both GW detector and AI-based experiments. In consid-

ering a site, practical concerns such as feasibility of installation and local infrastructure must

also be considered. Seismic noise has proven to be a major concern for AI and GW detection

[66,67]; for AI, vibrations during the launch and preparation translate into readout fluctua-

tions and spurious atomic phase from the retro-reflection mirror. Time-varying stray magnetic

fields and field gradients that create a difference in readout between gradiometers are a techni-

cal noise concern that must be addressed through shielding or active compensation; to this

end, a candidate site requires mapping and monitoring of magnetic fields and field gradi-

ents. Related to seismic noise, localized gravity gradient noise is an indistinguishable technical

noise for GW detection in the ELGAR observation band. This kind of noise can be separated

into seismic and atmospheric components, placing importance on local geographic and cli-

matic features of a candidate site. A site must be far from and protected against anthropogenic

noise; this noise is endemic throughout the ELGAR detector’s observation band. This is to

say that a potential detector site needs thorough characterization as well as monitoring of the

local and regional seismic, magnetic, and weather activity via various sensors. To fulfill these

different properties we consider different candidate sites in France and Italy: the low noise

laboratory Laboratoire Souterrain `

a Bas Bruit (LSBB) in Rustrel in France, and two former

mine complexes in Sos Enattos and Seruci located in Sardinia. All three sites are under exten-

sive study, with the LSBB hosting the MIGA equipment in two new specifically built 150 m

galleries. The LSBB was formed after the decommission of a launch control facility for the

French strategic nuclear deterrence; now a ground and underground scientific infrastructure

characterized by an ultra-low noise seismic and magnetic environment, the site fosters mul-

tidisciplinary interactions and approaches to fundamental and applied research with broad

scientific and industrial expertise [68]. This site is the location of the MIGA project [64],

where new galleries were blasted to allow for the full equipment installation. The Sos Enat-

tos and Seruci sites are located on Sardinia, an area of Europe with low population density,

low anthropogenic noise, and ancient geological structure with seismic activity among the

lowest on Earth [69]. The sites contain former mine shafts with useful infrastructure like mon-

itoring, ventilation, and elevator equipment and they are already undergoing measurement

campaigns for seismic, acoustic, and magnetic activity [69]. These sites are already under

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Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

consideration for the Einstein Telescope [12] and for the Ar40 distillation tower of the ARIS

project [70].

1.4.2. Atom optics. ELGAR operates as a network of differential phasemeters [51,64], where

each device consists of two AIs in a gradiometer configurationseparated by a baseline L, coher-

ently manipulated by the same circulating light fields propagating with wavenumber keff .An

incident GW modulates this baseline, leading to a differential phase shift between the two

AIs. To drive such an interferometer, the atom optics typically consist of composite pulses as

well as high-order Bragg/Bloch transitions. This enhances the wavenumber, keff =2nkl,cor-

responding to the relative momentum between the two arms of the interferometer, where kl

is the single-photon wavenumber of the driving light field. Any geometries for ELGAR share

similarities in that they involve atoms in free fall, show a linear scaling of the phase shift ver-

sus the effective wavenumber, and demonstrate a frequency dependent response on the pulse

separation time T. Geometries involving multiple loops lead to resonant enhancement [71]

and can suppress spurious phase terms [72–75], especially when combined with a useful tech-

nique for compensating the effects of static gravity gradients through a suitable frequency

change of some of the intermediate laser pulses [29,76–78]. The atom optics in AIs imprint

the phase of the applied light field onto the atomic wavefunction and can manipulate the inter-

nal state of the atom. Reaching the sensitivity target for ELGAR requires LMT, boosting keff.

The three most common atom optic techniques involve utilizing stimulated Raman transitions

[49], Bragg diffraction [79], Bloch oscillations [80], or a combination of the three for LMT

[81–90]. In addition, single-photon processes have been proposed to combat typically high

requirements on the laser frequency noise [91] and demonstrated in atom interferometry [92]

including LMT [93]. Effective wave numbers equal to or in excess of 1000klby combining

Bragg diffraction and Bloch oscillations appear to be feasible based on the present state-of-

the-art [85]. The sensitivity garnered through this process can also be selectively enhanced by

switching from a broadband mode used in the detector to a resonant detection mode [71,94].

1.4.3. Atom source. Essential to the success of each individual interferometer is the atomic

source that feeds it [95]. The source affects the sensor sensitivity and defines the susceptibil-

ity to systematic effects. The generation of large ensembles at high flux is required to obtain

sufficient stability in an interrogation time as short as possible. The intrinsic noise of such a

two-mode sensor, with uncorrelatedinput states, is characterized by the standard quantum limit

(SQL) δφSQL ∼1/√nmeasN,wherenmeas is the number of interferometric measurements and

Nis the number of atoms. To reach the target sensitivity of 1 μrad/√HzforasingleAIat

the SQL, a flux of 1012 atoms per second is required. AIs typically employ the Alkali isotopes

of potassium (39K, 40Kand41K), rubidium (85Rb and 87Rb), cesium (133Cs) and lithium (6Li

and 7Li). The Alkali elements can be addressed with multiple cooling techniques that are path-

ways to ultracold temperatures. 87Rb is the workhorse of atom interferometryin a wide range of

application and is the baseline species considered in this proposal. State-of-the-art atom optics

techniques are typically tested with 87Rb; of particular interest is the lowest effective tempera-

ture of a few tens of picokelvin (pK) demonstrated with 87Rb [96,97]. Cesium 133 is another

promising candidate, similar to 87Rb, having shown applicability to LMT experiments like

those measuring the hyperfine structure constant [98]. Achieving the required ultra-cold tem-

peratures with Cs is, however, a difficult task due to its scattering length complicating an evap-

orative cooling process. Alkaline-earth atoms and transition metals/lanthanoids that resemble

alkaline-earth atoms like strontium (87Sr and 88Sr) and ytterbium (171Yb) are typically used in

atomic clocks for their narrow linewidth optical transitions and show significant promise for

atom interferometry. These classes of atoms are immune to the quadratic Zeeman shift, setting

them apart from other species. LMT single-photon transitions have been demonstrated with

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

these species [92,93]. Prime candidatesfor an ELGAR detector based on alkaline-earth species

revolve around Sr and Yb isotopes. Atomic sources for the species under consideration typi-

cally take the form of a 2D+MOT fed either by a dispenser or an oven, which could be directly

loading the trap or going through a Zeeman slowing stage. The stringent flux requirements can

be relaxed by employing an atomic source that goes past the SQL—this can only be done by

using non-classical input state, so entangled state. Such an entangled source can be generated

via atom–light interactions like a quantum non-demolition measurement or cavity feedback

or through atomic collisions [99]. The most promising results have demonstrated an 18.5 dB

enhancement, what is equivalent to a 70-fold increase in the atomic flux [100,101]. A gain of 20

dB corresponds to a factor 100 reduction in the required atomic flux and is a very active line of

research worldwide.

1.4.4. Seismic isolation. GW detectors, with laser or matter-wave interferometry, maintain

the same fundamental principle of operation: the distance between two free falling inertial

test masses is precisely measured with a stable laser in order to detect tiny modulations

that can only be attributed to GWs. In the framework of ELGAR, the role of test masses

is played by the atoms which are in free fall, and therefore naturally isolated from seismic

vibrations. By comparison to optical GW detectors, using free falling test masses allows for

an important reduction of the impact of seismic noise at low frequencies. The first term of

equation (13) shows that seismic noise creates a spurious GW strain S1/2

h(ω) with a scale fac-

tor 2ω/c: at 1 Hz seismic noise is filtered by a factor ∼2×10−8m−1whereas in a ≃3km

laser interferometer like VIRGO this factor is ≃3×10−4m−1. In spite of this advantage, ade-

quate vibration isolation equipment is still required for an ELGAR detector due to the residual

coupling from vibrations of the retroreflecting mirrors and the beamsplitter: to reach the tar-

get sensitivity goals of ELGAR in the 0.1–1 Hz range, the limit on the displacement noise

of these elements needs to range from 5 ×10−11 mHz

−1/2at 0.1 Hz to 8 ×10−15 mHz

−1/2

at 1 Hz. These requirements are challenging, and so constitute an active line of research for

a terrestrial based AI based GW detector. A simple double suspension system [102] with

a resonance frequency at 10 mHz could begin to meet ELGAR requirements, but it would

require a 25 m simple pendulum—this is impractical and expensive. Due to geometric/space

requirements and the observation band of interest, a new solution is needed that is not a sim-

ple upgrade of the super attenuators in optical GW detectors [103]. One example ELGAR

mayfollowisthatofAIGO[102], where they demonstrate a compact isolation and sus-

pension system using two stages of horizontal pre-isolation and a single stage of vertical

isolation. This system consists of self-damping pendulums, Euler springs [104], and Nio-

bium ribbon suspension. Furthermore, the system employs a LaCoste linkage in vertical pre-

isolation [105], while the second stage of horizontal pre-isolation is based on a Roberts linkage

[106]. Such methods could possibly be further extended toward lower frequencies to meet the

requirements of ELGAR, but it will require coping with the issue of losses and anelasticity

[107,108].

2. ELGAR sensitivity and data

2.1. ELGAR operating parameters and sensitivity curve

The configuration parameters of the ELGAR detector corresponding to an atom shot noise

limited sensitivity of 3.3×10−22 Hz−1/2at the peak frequency of 1.7 Hz are summarised

in table 1. We list in table 2the noise requirements to reach such sensitivity that we subdi-

vided into three parts. The first line corresponds to the atom shot noise contribution that is, by

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Table 1. Parameters of the ELGAR detector to reach a strain sensitivity of 3.3×

10−22 Hz−1/2at the peak frequency of 1.7 Hz limited by atom shot noise.

Atomic source

Species 87Rb

Loading source 2D +MOT

Equivalent atomic fluxa1×1012 s−1

Ensemble type Ultracold source

Expansion velocity (Teff ≈100 pK) 100 μms

−1

Vertical launching velocity 4 m s−1

Cloud sizeb16 mm

Detector

Single gradiometer

Configuration Double loop, four pulses

Interrogation time 4T=800 ms

Atom optics Sequential Bragg

Momentum transfer 2n=1000 k

Baseline L=16.3km

Peak strain sensitivity (at 1.7 Hz) 4.1×10−21 Hz−1/2

Full detector

Number of gradiometers per arm N=80

Gradiometer separation δ=200 m

Total baseline LT=32.1km

Peak strain sensitivity (at 1.7 Hz) 3.3×10−22 Hz−1/2

a1×1010 s−1+20 dB squeezing (in variance) or 1 ×1012 s−1.

bAssuming 10 interleaved interferometers, 1 ×109atoms and 20 dB squeezing.

design, the dominant noise contribution. The second part (lines 2–7) accounts for the degree of

controllability of the atomic motion and of the atom optics, for their mutual couplings, and for

the couplings to the environment. The third part (lines 8–10) covers the influence of static

electric and magnetic fields to the atoms.

The details of the calculation of the requirements of table 2are given in [56]. We present

here the list of the different noise contributions for self-consistency. Equation (13)givesthe

link between the strain sensitivity of the whole detector and the phase noise level of a single

AI forming the array as:

Sh(ω)=1

√N×1

2nklL|ωG(ω)|×2S(ω), (14)

The target floor sensitivity level of 3.3×10−22/√Hz for the array of 2Nuncorrelated gra-

diometers corresponds to the strain sensitivity for a single gradiometer of 4.1×10−21/√Hz

which is reached at the peak frequency of 1.7 Hz. This, in turn, sets the differential atom phase

sensitivity limit of 2Slim

=√2×10−6rad/√Hz, with Slim

being the atom shot noise

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Table 2. Noise requirements for the ELGAR detector [56] to reach the designed strain

sensitivity.

Noise source Constraint

1. Phase noise from atom shot noisea1μrad Hz−1/2

2. Velocity noise (coupled to static rotation)b50 nm s−1Hz−1/2

3. Static relative beam alignmentc0.32 nrad

4. Compensation of static gravity gradientd1%

5. Relative beam angle jitter (coupled to imperfect velocity) 4 prad Hz−1/2

6. Laser beam pointing jitter (coupled to static gravity difference) 0.3 prad Hz−1/2

7. Wavefront curvature coupled to velocity noisee0.8 nm s−1Hz−1/2

Acceleration noise from:

8. Magnetic fieldf0.1 nT Hz−1/2

9. Blackbody radiationg2mKHz

−1/2

10. DC Stark shifth0.2 V m−1Hz−1/2

aBased on the equivalent atomic flux in table 1.

bAssuming a rotation rate of 73 μrad s−1(Earth rotation rate).

cAssuming an initial velocity noise of the atoms of 50 nm s−1Hz−1/2.

dGravity gradient Γ≈1.5×10−6s−2and assuming a source velocity noise of 50 nm s−1Hz−1/2.

eThe laser beam radius of curvature is 25 km (Gaussian beam waist of 50 mm).

fAssuming a magnetic field gradient of 1 nT m−1.

gAssuming a temperature gradient of 0.1 K m−1.

hAssuming an electric field gradient of 0.1 V m−2.

limited phase sensitivity of a single interferometer. In deriving the noise requirements, we

restrict the analysis to the case of a single interferometer and assume uncorrelated phase noise

between the interferometers forming the array. We set a conservative requirement for each of

the spurious phase noise contributions to not exceed the level of 0.1μrad/√Hz at 1.7 Hz for

a single AI. The main noise sources evaluated in reference [56]are:

•Couplings of Earth rotation (table 2, line 2), gravity gradients (line 4), beam misalignment

(line 3) and beam pointing jitter (line 5) to the initial position and velocity noise of the

atom source, and coupling of beam pointing jitter to gravitational acceleration differences

along the detector baseline (line 6);

•Magnetic fields, electric fields, blackbody radiation (lines 8, 9, 10)

•Impact of differential wavefront distortions (line 7);

•Scattered light and diffraction phase shifts (not in the table);

•Effect of inter-atomic interactions (not in the table).

The atom shot noise limited sensitivity curve of ELGAR, calculated with the parameters of

table 1, is illustrated in figure 5. For what concerns Seismic and NNs, the strategies adopted

to mitigate them below the atom shot noise are discussed in [56]. All the other noise sources

are then kept below atom shot noise according to the parameters of table 2. On the ELGAR

sensitivity curve, the interrogation time Tsets the corner frequency of maximum strain sensi-

tivity at 1.7 Hz. The resonance peaks correspond to the windowing effect of the AI captured

by the transfer function |ωG(ω)|[63]. As discussed in section 1.4.2, ELGAR can accommo-

date different geometries including single- and folded triple-loop to improve the sensitivity

at lower frequency or better suppression of the spurious phase terms. As shown in [56], by

varying slightly the interrogation time T, ELGAR can operate in broadband mode to detect

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 5. Strain sensitivities for different GW detectors, including ELGAR (atom shot

noise limit), aLIGO, ET and LISA; they cover the frequency range from 10 mHz to

10 Hz.

unknown GW signals and later switch to resonance mode to enhance the signals at specific

frequencies.

2.2. ELGAR within the global framework of GW detectors

ELGAR will complement the existing optical gravitational-wave instruments such as

AdvancedLIGO (aLIGO) and AdvancedVirgo (AdV), and the future detectors such as Einstein

Telescope (ET) and LISA, by covering a frequency band gap between the sensitivity curves

of ground-based and space detectors. The strain sensitivities for different detectors including

ELGAR, aLIGO, AdV, ET and LISA are illustrated in figure 5. As stated before, the reso-

nance peaks in the ELGAR sensitivity curve correspond to the windowing effect of the AI

and can be overcome by operating the antenna in a broadband mode [56]. The ground-based

detectors such as aLIGO or AdV are limited by seismic and thermal noises for frequency

below 10 Hz. The space-based detectors including LISA can operate at a much lower fre-

quency band from 0.1 Hz to mHz thanks to the large absence of Newtonian gravitational

fluctuations in space. ELGAR therefore offers a unique opportunity to explore GWs in the

deciHertz band where an ambitious science program can be carried out. The new possibil-

ity offered by ELGAR for astrophysics, gravity and fundamental physics will be detailed in

section 3.

2.3. Data management for the GW and geophysical, atmospheric and environmental

monitoring communities

The ELGAR detector will generate two kinds of data: the atom interferometry strain sensor

output, providing the time series h(t) of the GW induced strain, and a large number of ancillary

data from a whole range of environmental sensors. ELGAR will produce strain data at much

higher spatial resolution in a frequency band substantially lower than those of the existing

detectors. This offers the unique opportunity to compare this gravitational data with other local

measurements. Inversely the GW final strain data will benefit from the combination of existing

and new data, to disentangle the effect of GW from that of classical NN. The exploration of

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

the parameter space of gravitational-wave sources is a large-scale effort that involves many

research groups and relies on interaction between gravitational-wave source modeling groups

and the gravitational-wave data-analysis community.

State-of-the-art methods seek to address these challenges by considering data encoded

in large-scale matrices and employ tools like principal component analyses (PCA), singu-

lar value decomposition and non-negative matrix factorization. Despite their capabilities,

a number of inherent limitations characterize these approaches, including the inability to

encode high-dimensional observations or data from multiple sources/modalities. Further-

more, these approaches are data-agnostic, which limits their potential for the specific set-

ting. Within ELGAR, novel mathematical frameworks will be exploited and developed, by

modeling observation using high-dimensional data structures known as multi-way tensors,

investigating approaches like robust tensor PCA, and low-rank tensor recovery. Furthermore,

available observations could be exploited into a supervised machine learning algorithm in

order to introduce methods like deep tensor neural networks for the optimal representation

of measurements.

Specifically, the envisioned data management framework will offer a number of novel capa-

bilities in terms of multi-modal high-dimensional data observation quality enhancement. First,

it will support the separation of the contributionof different noise sources from the observations

by identifying the essential statistical characteristics, both in the time as well as the frequency

domain for each signal category. In addition, it will offer the ability to perform joint analysis

of multiple time series of in situ measurements from deployed sensing networks. By develop-

ing a unified framework, a variety of signals from disparate origins, represented in different

forms (e.g., time-series and imagery) will be (jointly) processed in order to characterize their

spatio-temporal evolution, and thereby facilitate the calculation of the geophysical computa-

tional models. Last, it will act as the core framework for the imputation of missing measure-

ment from different spatial locations and temporal instances, recovering lost measurements

due to sensor and/or storage failures, exploiting properties like model sparsity and low-rank

characteristics.

In addition to the enhancement of the quality of observations, the developed framework

will also support the clustering and detection of anomalies through cutting-edge signal model-

ing and learning. This objective will be achieved by autonomously generating the nominal

data space, considering key operational characteristics parameters of each sensor category

(e.g., nominal range of values, sensitivity, accuracy, and drift). Based on this information, the

sensing uncertainties will be automatically estimated, exploiting their representation in lower-

dimensional spaces, which will both automatically update the nominal operational bounds, as

well as indicate when specific regions of data exceed these bounds, due to the existence of short

(e.g. outlier) or longer (e.g., hardware) failure of the sensing infrastructure. To accommodate

the expected increased volume of the data collected and the expectation of providing reduced,

yet equivalently informational observations, we will employ cutting-edge machine learning

algorithms, focusing on deep learning architectures, for inferring the optimal anomaly detec-

tion policies in a completely unsupervised way [109]. Furthermore, the state-of-the-art could

be extented by simultaneously considering observations from multiple modalities/sources and

time-instances [110] into the anomaly detection policies.

For supporting the above goals, the data storage and access needs of ELGAR will be stud-

ied in order to propose the proper storage and computing infrastructure to meet them. In order

to estimate infrastructure requirements, the landscape of the ELGAR’s data will be analyzed

in four dimensions: (a) their size, (b) their access patterns, (c) their processing needs, and (d)

the robustness of the proposed approach(es). Then the serving model of the data will be ana-

lyzed along with the different computing infrastructure options that can better serve the data

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

requirements. User-friendly and customizable ways to access the data and formulate informa-

tion needs will also be consider, mainly based on the ontology-based data access paradigm and

exploratory approaches, allowing the integration and interoperation among different scientists

and data repositories.

3. Astronomy and physics with ELGAR

The first few years of GW astronomy, made possible by the large optical instruments LIGO [8]

and Virgo [9], have significantly altered our knowledge and expectations about GW sources.

The first detection, the GW150914 event [1], consisting of a pair of 36M+29MBHs,

merging into a final 62MBH, and the subsequent multiple GW observations have demon-

strated that binary BH (BBH) signals are by a factor O(10) the dominant component of the

observed mass spectrum [111] of GW sources. Earlier, BNS coalescences were considered

the most likely source of GWs: the period evolution in systems like the Hulse–Taylor binary

pulsar (PSR B1913 +16) with the predicted loss of orbital energy had provided indirect

confirmation of the emission mechanism [112](seealso[113]), and the observational evi-

dence, by way of the pulsar phenomenon, of several BNS systems in our Galaxy resulted in

a credible estimate for an event rate [114,115]. These predictions were actually confirmed

when in the summer of 2017 LIGO and Virgo observed the first BNS event [116], yet BBH

events remain prevalent. The abundance of BBH events is a posteriori understandable: the

GW signal amplitude scales roughly as h∝M5/3, hence a ∼30 +30MBBH system is

roughly detectable O(10) farther away than a 10 +10MBBH system, previously taken as

a benchmark. The observed volume scales approximately with the cube of the maximum

observable distance, which explains the observed O(103) rate enhancement over the bench-

mark. We remark that even a single BNS observation, GW170817 [116,117], has had an

immense scientific value, also thanks to the association with a gamma-ray burst [117], con-

firming a long standing hypothesis about the gamma-ray burst (GRB) origin [118]. From the

LIGO-Virgo observations during the two first observing runs [111], O1 and O2, the merger

rate estimated for BNSs is 110–3840 Gpc−3yr−1(90%confidence intervals), and for BBHs

is 9.7–101 Gpc−3yr−1. Given that there are no established detections for BH–NS merg-

ers, only upper limits can be established and all of them (also 90%confidence intervals) are

below 610 Gpc−3yr−1.

The observations of LIGO and Virgo belong to the high-frequencyband, between 1–104Hz,

although current sensitivities do not go below 20 Hz. There are two other bands where there is

significant progress toward the direct direction of GWs: (i) the low frequency band, between

10−5–1 Hz, not accessible from ground due to seismic and gravity-gradient noises, where

space-based detectors can operate. (ii) The very-low frequency band, between 10−9–10−6Hz,

the realm of pulsar timing arrays (PTAs). The low-frequency band has already a space mis-

sion selected (on June 2017), the Laser Interferometer Space Antenna (LISA) [119], the L3

mission of the European Space Agency with a launch date expected in 2034. LISA will

consist in a triangular constellation of three spacecrafts exchanging laser beams and 2.5 mil-

lion km of arm-length trailing the Earth on a heliocentric orbit. The required sensitivity is

attained by suppressing the laser frequency noise below the secondary noises by a combi-

nation of laser frequency locking and noise cancellation via time-delay interferometry. The

LISA Pathfinder mission [120–122] has demonstrated, between December 3, 2015 and June

20, 2017, the main technology for LISA. LISA has a very wide science case as described in

the white paper The Gravitational Universe [123]. On the other hand, in the very-low fre-

quency band several consortia of radiotelescopes measure, over long time spans, the time of

arrival of radio-pulses emitted by well-chosen sets of (millisecond) pulsars. By correlating

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

the measurements from the different pulsars, deviations in the times of arrival of the radio-

pulses due to passing GWs are sought. There are three PTA collaborations: the European

PTA (EPTA [124]), the North American Nanohertz Observatory for GWs (NANOGrav [125]),

and the Parkes PTA (PPTA [126]). They form the International PTA (IPTA [127]) with the

aim of enhancing the sensitivity by combining the data of the individual PTAs. The sensi-

tivity of these PTAs is already inside the predicted discovery space for GW backgrounds

produced by the emission of inspiraling supermassive BH binaries, with masses between

108–1010M.

The decihertz GW band, between 0.1–10 Hz, where we do not have any current detector

(not even approved for construction), is very rich in GW sources, which is reflected in the

fact that it is the bridge between two distinctive GW bands in terms of sources, the high-

frequency band, where second-generation ground based detectors have already observed a

number of sources [111], and the low-frequency band, where LISA [119] will operate. The

main sources for this band, as it happens with the high- and low-frequency bands, are coalesc-

ing compact binaries. The components of these binaries can be diverse: mainly white dwarfs,

NSs and BHs. Among the BHs we have to differentiate them according to mass (stellar-mass

BHs and intermediate-mass BHs) and origin (stellar origin, globular clusters, early Universe).

It is also important to understand to which stages of BBH coalescence (inspiral, merger and

ringdown) ELGAR is sensitive. In principle, ELGAR should detect: (i) the merger (and ring-

down) of intermediate mass BBHs (with masses in the range 102to104M). (ii) The inspi-

ral phase of stellar-mass binaries, like BBH coalescence; BNS coalescence; neutron star-BH

coalescences; even binaries containing white dwarfs. (iii) Stochastic gravitational-wave back-

grounds for ELGAR. We have to distinguish backgrounds due to the emission of many com-

pact binary inspirals from those produced during the early-universe by means of high-energy

processes.

3.1. Extending the BBH spectrum

The large number of BBHs already detected in the scientific runs of the LIGO and Virgo

detectors (from O1 to the current O3 runs) motivates a considerable effort to better under-

stand the origin of these systems, whether they result from the common evolution of pairs

of massive stars, or form through capture mechanism in dense stellar environments [128]. To

fully answer these questions, we want to characterise and extend the mass spectrum of these

systems: are BBH pairs like GW150914 the most massive we should expect? Are there more

massive systems to be detected, that we cannot just see yet? And it is important to measure

accurately parameters like spin magnitudes and directions, which carry information about the

past evolution of the system.

To address these questions meaningfully, it is necessary to enlarge the window of obser-

vation toward lower frequencies, since the maximum frequency of the GWs emitted roughly

scales as M−1; an event 30 times more massive than GW150914 would be confined at fre-

quencies below ∼10 Hz, where LIGO and Virgo are essentially blind because of seismic and

suspension thermal noise. In the long term, the ground-based Einstein Telescope (ET) [12]

will push the lower frequency limit down to ∼3 Hz, thus considerably widening the range of

detectable masses [129], whereas the space based LISA detector [119] will open up the mHz to

Hz range to observation, making possible to detect very massive systems, and extreme events

like the infall of matter into supermassive BHs.

However, we can see in figure 6that a gap will remain which could prevent, for instance,

to directly observe the merger phase of the so-called intermediate mass BHs (IMBH), systems

including BHs of O(103M). Filling this gap is one of the purposes of an AI designed for the

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 6. Design sensitivity of the second-generation ground-based detectors LIGO and

Virgo, the future third-generation ground-based detector ET, and of the future space-

based detector LISA, along with the trace of the BBH event GW150914, of an hypo-

thetical IMBH event at 3 Gpc, and spectra of BNS events. Figure obtained using the

GWplotter tool [130].

detection of GWs; evidence for such systems could shed light on the possible existence of a

ladder of BH masses, from stellar mass to supermassive ones. An absence of evidence could

indicate that entirely different formation mechanisms are at play in different mass ranges.

We can predict the waveforms emitted by massive BBHs; considering that the only relevant

physical parameters are the Newton constant GNand the speed of light c, from dimensional

analysis only we have that

h(t,d,M1,M2,S1,S2)=ht

GNμc−3,d

GNμc−2,M1

μ,M2

μ,S1

GNμ2c−1,S2

GNμ2c−1, (15)

where S1,2,M1,2 are the BHs spins and masses, and μis an arbitrary mass scale. In a system

(say) λtimes more massive than a reference one (could be GW150914 for instance), noticing

that the waveform is independent of μ, the equivalence holds

ht,d,λM1,λM2,λ2S1,λ2S2=ht

λ,d

λ,M1,M2,S1,S2.(16)

In the frequency domain

h(f,d,λM1,λM2)≡+∞

−∞

h(t

λ,d

λ,M1,M2)e−2πift dt

=λ+∞

−∞

h(τ,d

λ,M1,M2)e−2πiλfτdτ=λ2ˆ

h(λf,d,M1,M2), (17)

where in the last equation we have exploited the 1

ddependency of the waveform on distance.

Hence the frequency evolution fl→fufor a system with masses λM1,2 is mapped onto the

evolution λfl→λfuof a system with masses M1,2 at the same distance, including a λ2factor

on amplitude and λscaling in the frequency. It follows a scaling by λ3/2of the SNR:

SNR ≡2



fu



h(f,d,λM1,λM2)

Sn(f)df=2λ3/2



λfu

λfl



h(ν,d,M1,M2

Sn(ν/λ)dν. (18)

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

For instance, a 103+103MBBH (λ≃30 with respect to GW150914), located at 3 Gpc

could be observed in the band 1–10 Hz with SNR ≃5 using a detector having a noise floor

O(10−21 Hz−1/2); even though this noise floor is 100 times worse than Advanced LIGO or

Virgo, the longer duration in band of the signal would allow to accumulate a comparable

SNR.

3.2. Binaries of intermediate-mass BHs

The size of a massive BH (MBH) in comparison with its host Galaxy is tiny. For instance, for

an MBH with a mass of 106Mthe difference spans over ten orders of magnitude. In spite of

this, there is a link between the properties of the host Galaxy and the MBH. The mass of the

MBH and the velocity dispersion σof the spheroidal component is one of the best examples

[131]. However, the low end of this mass-sigma correlation is uncertain because we lack data.

By extending this correlation to smaller systems, we expect that dense stellar systems such as

clusters harbor intermediate-mass BHs, IMBHs, i.e. BHs with masses 102–104M(see [132]

for a review).

For two IMBHs to form a binary emitting GWs, there are two different possibilities. First,

(i) two host clusters born in a cluster of clusters, as those which we observe in the Antennæ

Galaxy (see introduction of [133]), can be gravitationally bound, and doomed to merge with

each other. In this process, the IMBHs sink to the center of the system due to dynamical fric-

tion first, to form a BBH, and later that binary shrinks its semi-major axis due to interactions

with stars. After each of such interactions the star can take away a bit of the energy of the

BBH. If there are enough stars to interact with, the BBH evolves and eventually enters the

GW-dominated regime. This means that the main driving mechanism in the evolution of the

BBH are GWs, so that the orbit circularizes. This process has been described in the works

of [133–135]. A space-based observatory such as LISA should detect these systems with an

event rate of 4–5 yr−1. Another possibility for a BBH to form is (ii) via the runaway forma-

tion of two very massive stars in a single cluster with a binary fraction of 10%, as described

in [136]. In [137] it is estimated that LISA and Advanced LIGO should detect tens of them,

but this depends on the distribution of the masses of the host cluster and also their central

densities.

In [139] it is shown that a BBH can spend a significant amount of its evolution before the

merger in the decihertz regime. In figure 7we show two BBHs spending a significant amount

of their evolution before the merger in the ELGAR regime. This means that these systems

are perfect targets for ELGAR. A joint detection of these BBHs with ELGAR and the early

inspiral with LISA would help to obtain enhanced measurements of the parameters and also

to potentially break degeneracies. We can see on the right panel that the system merges out of

the LISA window, and spends 8 min in the ELGAR sensitivity window and merges at about

1 Hz. This means that if an observatory such as LISA is operative at the same time as ELGAR,

it could issue a warning years in advance with a precision of seconds.

3.3. Intermediate-mass ratio inspirals

Compact objects such as stellar-mass BHs, neutron stars or white dwarfs can form a binary with

an MBH and contrary to extended stars, approach closer distances without suffering significant

tidal stresses. In the process the binary system emits gravitational radiation as orbital energy is

lost. Such radiation provides us with detailed information about the binary and allows us to test

gravity in the strong regime. Due to the mass ratio, we talk about extreme-mass ratio inspirals

because q104: 1 (EMRI, see [140,141]). Such EMRIs are one of the main objectives of

LISA [119] and form in galactic nuclei.

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 7. Left panel: characteristic amplitude hcas a function of frequency for a BBH

of masses 4000Mand 5000M. We show the initial dynamical parameters on the two

left corners. The BBH initially has an eccentricity of e0=0.4, an initial semi-major axis

of a0=10−3pc and are is located at a distance of D=1 Gpc. We show the sensitivity

curve for ELGAR starting at 10−3Hz and hc∼10−14. We also show the curve for LISA

starting at the lowest frequency, the ET starting at 1 Hz and LIGO, at 10 Hz. We display

the first harmonics of the GW in the approximation of [138] and show different moments

in the evolution with circles on the top of the second one. The last diamond corresponds

to one year before the merger. At each of these, we additionally give the eccentricity

and the periapsis distance normalised to the Schwarzschild radius. The source enters the

ELGAR regime 5 min before merger. Right panel: same as the left panel but for slightly

different masses, and 8 min before merger.

Smaller mass ratios, of q∼102–104: 1 correspond to intermediate-mass ratio inspirals

(IMRIs, see e.g. [142–144]), and are optimal sources of ELGAR. IMRIs form in smaller sys-

tems, in globular clusters, with typically very high eccentricities, via two-body relaxation or

the braking mechanism, i.e. the parabolic formation of a binary, as described in [145–151]).

The work of [152] is the first numerical simulation which shows the formation and evolution

of an IMRI in a globular cluster. The authors observe a binary of a stellar-mass BH of mass

26Mforming with the central IMBH, of mass MBH =500Mwith an initial semi-major axis

of a∼10−5pc and an eccentricity of e=0.999, which fits in the parabolic capture mechanism

of [146]. Due to the relativistic recoil [153–155], the merged system leaves the whole cluster.

After this initial paper, other independent groups have found similar results, such as [156,157].

In particular, the simulations of [158] are basically a reproduction of the set-up of [152]but

with a different numerical scheme which however remarkably leads to a very similar result.

Ground-based detectors such as the proposed ET [12,159] (with SNRs of up to ∼2000, and

are of typically a few hundred and of tens for masses up to 2000M) but also LIGO and Virgo,

can detect the final stages in the evolution of IMRIs (with SNRs of a few tens) and, depending

on the eccentricity, jointly with LISA (with SNRs of a few to tens), as shown in [160]. Due to

the range of frequencies that these sources have, a decihertz observatory such as ELGAR will

have an important impact. In figure 8we show the characteristic amplitude in function of the

frequency of an IMRI, as well as a few different moments in the evolution.

It has also been shown in the work of [160] that by adding a decihertz observatory such

as ELGAR, we can impose better constraints on the system’s parameters. LISA and, later,

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 8. Same as figure 7but for an IMRI of masses 1000Mand 10M. The initial

eccentricity is of e0=0.998, as we expect from these systems (see [140,160]), and an

initial semi-major axis of a0=10−3pc. The IMRI spends 1.5 h in the ELGAR regime.

LISA can forewarn ELGAR years in advance and with at least seconds of precision about

the time when the source enters in its domain and provide detailed information about all

dynamical parameters of the system.

ELGAR can measure the inspiral and hence derive parameters such as e.g. the chirp mass. At

more advanced stages in the evolution, LIGO/Virgo can detect the merger and ringdown, which

allows us to derive the final mass and spin. Due to this combined detection, and contrary to an

individual one, one could break various degeneracies and obtain enhanced measurements of

the parameters.

3.4. Stellar-mass binaries

The LIGO and Virgo observatories cannot currently discern the formation channel of stellar-

mass BBHs. In [161] it is shown that BBHs formed either dynamically or in the field via

stellar evolution share identical properties, i.e. masses larger than the nominal 10M,amass

ratio (q≡M2/M1) of about 1, low spin, and nearly circular orbits.

A compound detection of these detectors with LISA could allow us to to study different

moments in the evolution of BBHs on their way to coalescence [119]. LISA can detect BBHs

when the BHs are still 102–103Schwarzschild radii apart, years to weeks before they enter the

LIGO/Virgo band. At such separations, the orbital eccentricity in principle bears the imprint of

the formation channel because (i) BBHs in dense stellar systems form on systematically more

eccentric orbits and (ii) the GW radiation at this stage is too weak to circularize the orbits.

Therefore, aprioridetecting circular binaries with LISA typically would imply a formation in

the field, while a detection of LISA of eccentric ones should have formed dynamically.

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 9. Same as figure 7but for a BBH of masses 10Mand 30M. The system

enters the ELGAR sensitivity curve five days before merger, and starting at about 0.3Hz,

crosses most of it in frequency.

Nevertheless BBHs formed dynamically stand a big chance of eluding the LISA band, as

shown in [162]. Indeed, in their work the authors show that only a very small subset of the

detections would lead to a joint detection with LISA and LIGO/Virgo. This means that, even

if we successfully detect BBHs with LISA and LIGO/Virgo, we still will not be able to dis-

entangle the nature of their formation. This is a consequence of LISA not being able to detect

very eccentric BBHs, as shown in the work of [162], in particular their figure 1. In figure 9

we show a BBHs with an initial low eccentricity. A decihertz detector such as ELGAR would

contribute to recover the information about the formation process of the binary.

3.5. Horizon reach of ELGAR for compact binary coalescence

Ground-based detectors are currently sensitive to BBH coalescence at cosmological distance

distances where cosmological effects become relevant (z∼2). A measure of the capabilities

of a given detector is the distance reach it has to compact binary coalescence (CBC) events.

Here we show the horizon distance at which ELGAR can detect CBC events, for a given SNR

threshold, in terms of the total mass of the system (as measured in the source frame). The

horizon distance is the farthest luminosity distance at which a given source can be seen. That

is, we are assuming optimal sky orientation and localization. For the estimation of the ELGAR

horizon distance we adopt the ELGAR sensitivity shown in figure 5. In order to make this

computations we have used two different GW inspiral distance calculator tools [163,164](see

[165] for details), which we have adapted to the needs of this paper. In this way, by comparing

the results from the two libraries we make sure that the answers we obtain are correct. These

two libraries use in turn the LIGO Algorithm Library (LAL) [166]. To make the calculations

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 10. The plot shows the horizon redshift (in linear scale) for ELGAR detections

of CBC events in terms of the total mass in the source frame (expressed in units of the

Sun mass) for six different SNR detection thresholds (5, 8, 10, 20, 50, and 100).

we need to use gravitational waveforms for the CBC events. The ones we have used for the

inspiral-merger-ringdown(IMR) belong to the IMR-PhenomD waveforms introduced in [167],

assuming no spins. For the cosmology we have used the cosmological parameters quoted by

the 2015 Planck Collaboration paper [168].

In figure 10 we show the horizon redshift in terms of the total mass (as measured in the

source frame and in units of the Sun mass) for different SNRs (from 8 to 250). As we can see,

assuming the detection threshold is set at SNR =8, we can detect BBH coalescence beyond

redshift z=4. In figure 11 we show an equivalent plot, in the sense that we show the hori-

zon luminosity distance instead of the horizon redshift for ELGAR, where it is shown that

ELGAR can reach distances beyond 10 Gpc. Both plots show that ELGAR is most sensitive

to coalescing binary systems with a total mass in the range 103–104M.

3.6. Stochastic backgrounds of GWs

The incoherent sum of numerous unresolved GW signals results in a stochastic background of

GWs [169,170]. We can distinguish two types of stochastic GW backgrounds: (i) originated

by high-energy processes in the early Universe: from the inflationary epoch to different phase

transitions; spacetime defects of cosmological scales such as cosmic strings, etc. The energy

scale of the processes associated to these physical processes is around ∼103TeV (in con-

trast with LISA, around ∼10 TeV, and LIGO/Virgo, around ∼105TeV). (ii) Backgrounds of

astrophysical origin, produced by supernovae, magnetars, or the inspiral and merger of com-

pact objects (NSs or BHs). Depending on the event rate of these astrophysical GW sources

there may create a GW background overlapping the sensitivity band of ELGAR.

3.7. Observing type Ia supernovae

Another source of interest at low frequencies is represented by the type Ia supernova events,

expected to emit GWs and neutrinos [171] at frequencies in the gap between terrestrial large

optical interferometers and the space detector LISA, as shown in figure 12, where we plot the

range of signal strengths for galactic sources.

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Figure 11. The plot shows the horizon luminosity distance (in logarithmic scale) for

ELGAR detections of CBC events in terms of the total mass in the source frame

(expressed in units of the Sun mass) for six different SNR detection thresholds (5, 8,

10, 20, 50, and 100).

Figure 12. Type Ia and type II supernovae signal spectra, plotted against detector

sensitivities. Figure obtained using the GWplotter tool [130].

Again, these are signals potentially accessible for a detector with sensitivities close to

10−21 Hz−1/2, exactly as type II (core-collapse) galactic supernovae are potentially accessi-

ble to LIGO and Virgo. Type Ia supernovae are about as frequent as core-collapse ones, with a

frequency in our Galaxy about one per hundred years; therefore the chances for detection are

relatively modest, since the odds of detecting events in other galaxies are very unfavourable.

Yet, like is the case for core-collapse supernovae, even the detection of a single event could

provide a wealth of information on the detonation mechanism [171].

3.8. Multimessenger and multiband GW astronomy with ELGAR

Following the detections of the LIGO and Virgo detectors, we expect that several astrophys-

ical sources of GW transient signals will also emit electromagnetic (and possibly neutrino)

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

counterpart signals [172,173] that may detected by GW detectors, in particular by ELGAR.

These counterparts (including cosmic rays) will be crucial to maximize the discovery poten-

tial of GW detectors, providing a complementary knowledge of astrophysical GW events and

the emission mechanisms. The main candidate for electromagnetic counterparts in the case

of ELGAR will be binary systems containing an NS which may give rise to the emission of

GRBs. In the case of ELGAR, BNSs will not merge inside the band, so we are looking at IMRIs

containing an NS.

On the other hand, there are sources of GWs that can be observed in two different bands

of the GW spectrum by two different observatories at different times. This has already been

suggested between the high-frequency and low-frequency band [10], in the sense that the coa-

lescence of BBHs may be seen before by an observatory like LISA in the frequency band,

specially if the masses of these BHs is at the high-end of what LIGO has been observing, as

in the first detection of GWs [1]. With LISA observations we can determine the time of coa-

lescence and inform ground-based detectors operating at higher frequencies. Examples of this

have been already discussed in the previous subsections. Given that ELGAR is between the

low- and high-frequency bands, we have two different possibilities of multiband detections

where ELGAR could take part. ELGAR could detect binaries previously detected at the low-

frequency band and also binaries that later will be detected by high-frequency detectors (either

second-generation ones like LIGO [8], Virgo [9], and KAGRA or third-generation ones like

ET [12] or cosmic explorer (CE) [174]).

3.9. Fundamental physics with ELGAR

GWs offer many different ways of doing fundamental physics [175,176]. We can distinguish

different types of questions that we can address with GWs depending on the system we are

looking at and the assumptions we make about the systems itself. For instance, if we distin-

guish between the generation and propagation of the GWs we can see that different types of

physics can influence these physical processes and hence they have a very different impact in

the waveforms of the radiation emitted. If we look at the propagation of GWs coming from

distant sources we can test different types of what we can call fundamental physics: tests of

possible violations of Lorentz invariance; test of the existence of extra polarizations of GWs;

to bounds on a hypothetical graviton mass (our best estimate, mg<7.7×10−23 eV/c2,comes

from gravitational-wave observations [177,178]); tests of parity violations, etc. This type of

new physics is usually associated with different theories that predict the presence of extra

degrees of freedom, either coming from low-energy limit of quantum gravity theories or from

phenomenological models inspired by quantum gravity.

On the other hand, by looking at the late inspiral, merger and ringdown of compact binaries

includingBHs we can perform tests of the nature of compact objects (in particular of the no-hair

conjecturefor BHs) and also of the most non-linearand dynamical (radiative) regimeof general

relativity, not accessible to other types of observatories. We can also investigate whether certain

modifications of general relativity are correct and/or put bounds on them. The late inspiral

and merger require the use of numerical relativity or precise perturbative methods (like the

effective-one-body approach that incorporates information from post-Newtonian theory, BH

perturbation theory, and numerical relativity) and allow for tests of the nature of the compact

objects and the theory of gravity. If these binary systems involve neutron stars we can also try

to constraint the possible equation of state, which is currently not known, and which can tell

us about properties of matter and high-energy physics interactions. In the case of BH binaries

we can also put bounds on exotic horizonless objects proposed as alternatives to BHs (see, e.g.

[179]), as for instance boson stars, gravastars, fuzzballs, etc. Also, the final ringdown when the

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

deformed BH from the coalescence relaxes to its equilibrium state (a Kerr BH assuming general

relativity and the validity of the no-hair conjecture) via damped oscillations, the quasi-normal

modes, can allow us to perform fine tests of the no hair conjecture. The idea is simple, the

quasi-normal modes are determined by the characteristic frequency of the oscillations and the

characteristic damping time. These in turn have been precisely computed in general relativity

(and in other alternative theories) for BHs and some alternatives to BHs. Then, we can make

as many tests as different quasinormal mode frequencies and damping times are we able to

estimate from the GW signal.

Another test of the nature of compact objects and gravity can come from the detections of

IMRIs with ELGAR. This goes in the line of what has already been proposed for EMRIs and

space-based detectors like LISA (see, e.g. [180–182]). There, it was estimated that during the

last year before plunge an EMRI can spend of the order of ∼qcycles (105in the case of a

10Minspiraling into a 106MMBH). It means that the GWs emitted carry a detailed map

of the geometry of the MBH that allows for highly accurate estimations of the main EMRI

parameters and even estimations the quadrupole and high-order multipoles [180–182]. For the

Kerr metric, there are two sets of gravitational multipole moments, the mass and current (spin)

moments, {M}=0,...,∞and {J}=0,...,∞respectively, that satisfy the following simple sets

of relationships: M+iJ=MBH(iJBH),whereMBH and JBH are the mass and spin angular

momentum of the MBH. Therefore, if we are able to measure Nmultipole moments from the

GW signal we can perform N−2 tests of the geometry of the Kerr BHs. We can extend this

program to the case of IMRIs, where the number of cycles in the strong field regime should

be of the order of ∼102–104. In this strong field regime, and in contrast with EMRIs, both

the spin–orbit and spin–spin interactions are expected to be important, adding new time scales

to the problem and increasing its complexity, both in terms of the structure of gravitational

waveforms emitted but also in terms of the modeling required. The EMRI modeling program

is today an ongoing program based on the self-force approach that uses BH perturbation theory

developments up to second order in the mass ratio. In the case of IMRIs, the smaller mass ratios

indicate that perturbation theory alone will not be sufficient and a combination of pertubative

methods with numerical relativity will be needed.

Apart from tests on the nature of the most compact objects and the theory of gravity, ELGAR

can also contribute to another important problem in fundamental physics: The nature of DM.

There have been proposed different ways in which GWs can provide information about DM

[183]. We are going to mention here only the ones that are relevant for ELGAR. (i) Primor-

dial BHs (PBHs). There are many high-energy models with implications to early-Universe

cosmology which predict the formation of BHs less than 1 s after the big bang in the mass

range 10−16–106M. PBHs have been proposed by different authors as a candidate for DM,

some assuming a single mass scenario and others with a certain mass distribution. Using

different types of observations, a number of constraints on the fraction of DM that can be

made out of PBHs (see, e.g. [183]) have been derived. On the other hand, there are many dif-

ferent formation scenarios that may be distinguished by inferring the PBH mass spectrum.

Each formation scenario may lead to different gravitational-wave signatures. In this sense,

it is important to mention that there are two cases of GW detections in which we can be

sure that they are not due to BHs of astrophysical origin: the detection of nearby mergers

of sub-solar mass BHs with ground-based detectors and BBH mergers at very high redshift

(z>40) by future third-generation ground-based detectors like ET and CE (and similarly with

space-based detectors like LISA). Even in the case where PBHs do not constitute all of the

DM, they can still be connected to DM by forming different types of particle DM mini-halos,

whose annihilation may be enhanced giving rise, for instance, to gamma-ray emission. (ii)

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Environmental effects. There is the possibility that in the strong-gravity phase of the merger of

BHs and/or neutron stars DM may play a role introducing small effects in the emitted gravi-

tational waveforms. The question here is whether we can distinguish the DM environmental

effect from other possible environmental effects [184]. (iii) Exotic binary mergers.IfDMis

made out of some kind of particles, it is possible to conceive compact horizonless objects

made out of them. The coalescence of these objects may give rise to gravitational waveforms

different from those corresponding to BHs and neutron stars. This hypothetical scenario is

clearly linked to the program of testing the nature of the most compact objects in the cosmos.

(iv) Non-perturbative DM dynamics. DM particles may be produced non-perturbatively in the

early Universe giving rise to characteristic stochastic GW backgrounds. The question in this

case is whether these DM stochastic backgrounds can be distinguished from other stochastic

backgrounds, something depends strongly on the shapes of the spectra. (v) Phase transitions.

They are one of the possible causes of stochastic backgrounds of GWs of primordial original.

Given that the standard model of particle physics does not allow for first-order phase transi-

tion, detecting a stochastic GW background of this kind means new physics. If such transition

is associated with DM particles then we can infer some of the properties from the observations

of the GW background.

4. Conclusions

In this paper, we have proposed a European research infrastructure for the observation of GWs

in the deciHertz band, between 0.1–10 Hz. ELGAR will be based on the latest developments

of quantum physics and will use a geometry based on an 2D array of AIs. These techniques

offer important perspectives to limit the impact of seismic noise and NN, which are expected

to be major limitations for GW detectors at low frequency. Based on the preliminary design

presented in this paper, an ELGAR detector tens of km long could achieve a sensitivity of

3.3×10−22/√Hz at 1.7 Hz, assuming key developments in cold atom technologies mainly

related to source parameters and atomic manipulation, but also improvements in NN reduction

techniques.

Opening GW detection in the in the deciHertz band, ELGAR will then fill the gap in the

GW spectrum between ground-baseddetectorslike Virgo and LIGO(high-frequencyband) and

space-based detectors like LISA (low-frequency band), where an ambitious science program

can be carried out. ELGAR will access a diverse variety of CBC, both from their nature (white

dwarfs, NSs, and BHs), their masses (from comparable mass to intermediate mass-ratio bina-

ries), the orbital stage (inspiral, merger, ringdown), and even their presumable origin (stellar

origin, globular clusters, early Universe). ELGAR will also be able to detect supernovae core

collapse and stochastic backgrounds of GWs, both from astrophysical and early-universe ori-

gin. ELGAR should thus be able to answer relevant questions in astrophysics and cosmology,

concerning for example the existence of intermediate-mass BHs and their possible formation

channels, and the existence of PBHs and the allowed mass ranges. The possibility of detect-

ing with ELGAR the merger and plunge of IMRIs containing neutron stars would make the

instrument a key resource for multi-band GW observations and for multimessenger observa-

tions. ELGAR will also have an important impact in fundamental physics, particularly for the

detection of mergers of intermediate-mass BHs and/or IMRIs with significant SNR. The pre-

cise parameter estimation for these sources will enable tests of the no-hair conjecture of BHs

and even tests of general relativity and alternative theories. Additionally, ELGAR may also

provide information about the nature of DM.

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

Acknowledgments

This work was realized with the financial support of the French State through the ‘Agence

Nationale de la Recherche’ (ANR) in the frame of the ‘MRSEI’ program (Pre-ELGAR

ANR-17-MRS5-0004-01) and the ‘Investissement d’Avenir’ program (Equipex MIGA: ANR-

11-EQPX-0028, IdEx Bordeaux—LAPHIA: ANR-10-IDEX-03-02). AB acknowledges sup-

port from the ANR (project EOSBECMR), IdEx Bordeaux—LAPHIA (project OE-TWR),

the QuantERA ERA-NET (project TAIOL) and the Aquitaine Region (projets IASIG3D and

USOFF). The work was also supported by the German Space Agency (DLR) with funds

provided by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enact-

ment of the German Bundestag under Grant Nos. 50WM1556, 50WM1956 and 50WP1706

as well as through the DLR Institutes DLR-SI and DLR-QT. XZ thanks the China Schol-

arships Council (No.201806010364) program for financial support. JJ thanks ‘Association

Nationale de la Recherche et de la Technologie’ for financial support (No.2018/1565). PA-S,

MN, and CFS acknowledge support from contracts ESP2015-67234-P and ESP2017-90084-P

from the Ministry of Economy and Business of Spain (MINECO), and from contract 2017-

SGR-1469 from AGAUR (Catalan government). LAS thanks Sorbonne Universit´

es (Emer-

gence project LORINVACC) and Conseil Scientifique de l’Observatoire de Paris for funding.

RG acknowledges Ville de Paris (Emergence programme HSENS-MWGRAV), ANR (project

PIMAI) and the Fundamental Physics and Gravitational Waves (PhyFOG) programme of

Observatoire de Paris for support. We also acknowledge networking support by the COST

actions GWverse CA16104 and AtomQT CA16221 (Horizon 2020 Framework Programme

of the European Union). DS gratefully acknowledges funding by the Federal Ministry of

Education and Research (BMBF) through the funding program Photonics Research Germany

under contract number 13N14875. SvAb, NG, SL, EMR, DS, and CS gratefully acknowl-

edge support by ‘Nieders¨

achsisches Vorab’ through the ‘Quantum- and Nano-Metrology

(QUANOMET)’ initiative within the project QT3, and through ‘Förderung von Wissenschaft

und Technik in Forschung und Lehre’ for the initial funding of research in the new DLR-

SI Institute, the CRC 1227 DQ-mat within the projects A05, B07 and B09, the Deutsche

Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence

Strategy—EXC-2123 QuantumFrontiers—390837967 (B2), and the German Space Agency

(DLR) with funds provided by the Federal Ministry for Economic Affairs and Energy (BMWi)

due to an enactment of the German Bundestag under Grants No. DLR 50WM1641 (PRIMUS-

III), 50WM1952 (QUANTUS-V-Fallturm), and 50WP1700 (BECCAL), 50WM1861 (CAL),

50WM2060 (CARIOQA) as well as 50RK1957 (QGYRO). FS, GMT and AV gratefully

acknowledge support by the Italian ‘Ministero dell’Istruzione, Universit`

a e Ricerca’ through

the funding program PRIN, under contract number 2015L33WAK_003. BL, VS, MK, and

AP gratefully acknowledge support by the Berlin School of Optical Sciences and Quan-

tum Technology (BOS.QT) and by the German Space Agency (DLR) with funds provided

by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enactment of

the German Bundestag under Grants No. 50WP1432 (QUANTUS-IV-MAIUS), 50WP1953

(QUANTUS-V-Fallturm), and 50WP1702 (BECCAL).

ORCID iDs

B Canuel https://orcid.org/0000-0002-1378-2334

S Abend https://orcid.org/0000-0001-9539-3780

F Badaracco https://orcid.org/0000-0001-8553-7904

Class. Quantum Grav. 37 (2020) 225017 B Canuel et al

A Bertoldi https://orcid.org/0000-0002-4839-0947

P Bouyer https://orcid.org/0000-0003-4458-0089

N Gaaloul https://orcid.org/0000-0001-8233-5848

C L Garrido Alzar https://orcid.org/0000-0003-3616-1845

RGeiger https://orcid.org/0000-0003-4678-7139

JHarms https://orcid.org/0000-0002-7332-9806

A Landragin https://orcid.org/0000-0002-2941-4982

B Leykauf https://orcid.org/0000-0002-4630-0602

S Loriani https://orcid.org/0000-0001-6660-960X

M Nofrarias https://orcid.org/0000-0003-1518-2196

P Papadakos https://orcid.org/0000-0001-8926-4229

F Pereira dos Santos https://orcid.org/0000-0003-0659-5028

A Peters https://orcid.org/0000-0001-5538-9250

M Prevedelli https://orcid.org/0000-0002-3136-2392

SRosat https://orcid.org/0000-0003-4606-2170

A Roura https://orcid.org/0000-0002-8049-8982

DOSabulsky https://orcid.org/0000-0001-7421-2821

D Schlippert https://orcid.org/0000-0003-2168-1776

L Sidorenkov https://orcid.org/0000-0001-5293-2780

J-N Siemß https://orcid.org/0000-0003-3038-3922

C F Sopuerta https://orcid.org/0000-0002-1779-4447

GMTino https://orcid.org/0000-0002-7944-9825

A Vicer´

ehttps://orcid.org/0000-0003-0624-6231

W von Klitzing https://orcid.org/0000-0001-6172-8407

XZou https://orcid.org/0000-0003-3026-2944

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