Gravitational-Wave Lunar Observatory for Cosmology

Karan Jani1 and Abraham Loeb2

1Department Physics & Astronomy, Vanderbilt University,2301 Vanderbilt Place, Nashville, TN, 37235, USA

2Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA

Several large-scale experimental facilities and space-missions are being suggested to probe theuniverse across the gravitational-wave (GW) spectrum. Here we propose Gravitational-wave LunarObservatory for Cosmology (GLOC) - the first concept design in the NASA Artemis era for a GWobservatory on the Moon. We find that a lunar-based observatory is ideal for probing GW frequenciesin the range between deci-Hz to 5 Hz, an astrophysically rich regime that is very challenging forboth Earth- and space-based detectors. GLOC can survey binaries with neutrons stars, stellar andintermediate-mass black holes to & 70% of the observable volume of our universe without significantbackground contamination. The sensitivity at O(1 Hz) allows a unique window into calibratingType Ia supernovae. Its unprecedented sensitivity would trace the Hubble expansion rate up toredshift z ∼ 3 and test General Relativity and ΛCDM cosmology up to z ∼ 100.

Introduction.— Observations from the first set ofsuccessful gravitational-wave (GW) experiments - LIGOand Virgo - have shown the far reaching impact of theGW spectrum from 10∼1000 Hz on fundamental physics,astronomy and cosmology [1]. In the next two decades,GW astronomy aim to probe the universe at lowerfrequencies and well beyond the sensitivity reach of thecurrent detectors. The proposals for Earth-based nextgeneration observatories include the Einstein Telescope[2] and Cosmic Explorer [3], which will constitute onthe scale of tens of km intereferometers with enhancedsensitivity up to ∼5 Hz. By early 2030s, space missionssuch as the Laser Interferometer Space Antenna (LISA)will open the GW spectrum in the milli-Hz regime [4],while the global network of Pulsar Timing Arrays [5]would be probing nano-Hz GW frequencies. Other space-based concepts have also been proposed to deeper probethe milli- to micro-Hz frequencies [6–8].

One of the most challenging spectral regimes tomeasure GWs is from deci-Hz to 1 Hz. This frequencyrange tends to be too low for Earth-based detectorsand too high for space missions. The universe offersa rich set of astrophysical sources in this regime [9],whose observations would lead to stringent tests ofgeneral relativity and physics beyond the StandardModel [10]. A few proposals have been put forwardfor a space-based deci-Hz detector with geocentric(SAGE [11]) and heliocentric (DECIGO [12], ALIA [13],DeciHz Observatory [10]) orbits, which rely on advancedtechnologies in the post-LISA era (2040s).

In this Letter, we propose a GW detector on theMoon whose primary goal is to access the deci-Hz range.With the advent of NASA’s Artemis1 and CommercialCrew2 programs, the time is ripe to consider fundamental

1 https://www.nasa.gov/specials/artemis/2 https://www.nasa.gov/exploration/commercial/crew/index.

html

physics experiments from the surface of the Moon.We find that the Moon offers an ideal environmentfor pursuing uninterrupted deci-Hz GW astronomy fordecades and will strongly complement with the Earth-and space-based network of telescopes. We suggest theacronym GLOC - Gravitational-wave Lunar Observatoryfor Cosmology, for a detector that would survey 30−80%of the observable volume of our universe for a wide-rangeof GW sources. In particular, GLOC will be able tomeasure the evolution of the Hubble parameter at high-redshfits without multi-messenger followups.

Gravitational-Wave Setup on the Moon.— The Moonoffers a natural environment for constructing a large-scaleinterferometer as a GW detector, and such a scenariohave been mentioned in the literature [14–16]. Theatmospheric pressure on the surface of the Moon duringsunrise is comparable to the currently implemented 8km ultra high vacuum (10−10 torr) at each of the LIGOfacilities [17]. After sunset, the atmospheric pressure onMoon scales down to 10−12 torr [18]. The presence ofvacuum just above Moon’s solid terrain provides a greatbenefit in extending the LIGO interferometer length atminimal cost.

The seismometers left from the Apollo missionssuggests that the Moon is much quieter than Earth(see [19] and the references within). At low-frequencies(0.1∼5 Hz), the seismic noise on the Moon is threeorders of magnitude lower than on Earth [20, 21].Seismic noise is a fundamental limitation for the low-frequency sensitivity of GW detectors on Earth. InaLIGO, the seismic noise dominates at frequencies . 10Hz. The next generation Earth-based experiments areintended to push the limit to ∼3 Hz through severalambitious improvements [22] using quantum squeezers[23], covering mirrors with cryogenics and buildingunderground tunnels [24, 25]. By including some of thesetechnological upgrades, GLOC can push the sensitivityto frequencies ∼0.1 Hz (deci-Hz). These frequencies are

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FIG. 1. Concept design for GLOC and predicted sensitivity. Left: Three end stations on the surface of the Moonforming the full triangular-shape GW detector. The end stations are separated by 40 km. Each end station will contain atest mirror and a laser, making GLOC equivalent of three interferoemters. Right: GW sensitivity (as characteristic strain) ofspace-based (LISA), Earth-based (aLIGO, ET, CE) and lunar-based (GLOC-optimal and conservative) detectors. Also plottedfor comparison are sensitivity curves of space-based deci-Hz concepts DECIGO, ALIA, and DeciHz Observatory (DO). Image ofMoon’s surface was adapted from Lunar Reconnaissance Orbiter (NASA/GSFC/ASU) and Earthrise from the Apollo archives.

too high to pursue with LISA-like space missions, as theyare fundamentally limited by the laser shot noise.

Unlike a similar setup on Earth, a lunar-based detectoris only weakly affected by environmental factors such aswinds or lightening. The detector is very mildly sensitiveto the gravitational pull from the Earth’s ocean waves.Therefore, we expect a near continuous operation ofGLOC (close to 100% duty-cycle). The Moon-quakesoccur at much lower frequencies [21] and thus shouldnot impact the GW sensitivity in the GLOC spectrum.Bombardment by cosmic rays and solar flares can be asource of non-Gaussian noise. To reduce this noise, theend stations securing the test mass and the optics can becoated with a magnetic shield to keep the excess chargegrounded. In addition, a cooling source can maintaina steady temperature and mitigate thermal expansion,as the temperature on the surface of the Moon changesfrom −130 C to 120 C in a day [26]. Alternatively,a few km long open lava tubes found on the Moon [27]can provide a natural infrastructure for setting up theintereferometer.

An additional advantage (thus far) is that the Moonis not corrupted by any unpredictable noise from humanactivities. The site selection for the detector should avoidterrain favorable for potential launches. In case of alock-loss in the interferometer, a lunar-based detector can

be brought back online from a control center on Earth.In the event of a serious hardware failure, parts of thedetector can be replaced and repaired by astronauts.The benefit of performing on-request maintenance isnot available for space-based GW detectors, makingthe Moon a better long-term investment. In addition,future space-missions to access the deci-Hz range arelimited in their lifetime (typically a few years), afterwhich the gravitational perturbation from solar systemobjects will disrupt their geometry. In contrast, a lunar-based detector can operate and be steadily improved fordecades. Because the science sensitivity of the lunar-detector is at low frequencies, the data transmission rateis only a magnitude more than that expected for thespace-mission like LISA.

GLOC Concept Design.— We adopt a design schematicsimilar to that in next-generation Earth-based detectorsCosmic Explorer (CE) and Einstein Telescope (ET). Asshown in the left panel of Fig. 1 (left), the arm-lengthof the interferometer is set at 40 km and the L-shapedadvanced LIGO (aLIGO) type intereferoemter is replacedby a triangular geometry. Each end station formingthe triangle will consists of a laser and two test masses.Therefore, the full GLOC would be equivalent of threeindependent detectors. The end stations can be designedas dorm shaped compartments that are temperature

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FIG. 2. Cosmological reach of GLOC in comovingcoordinates. The concentric circles represents thepercentage fraction of the comoving volume of the observableuniverse (Vobs = 1.22×104 Gpc3) out to a given cosmologicalredshift, with the outermost being the CMB [28]. Thehighlighted slices refer to the horizon redshifts in GLOC(optimal) for the corresponding GW sources at their detectionthreshold (SNR ≥ 8). The ones on the right areknown examples of binary sources with black holes (BHs)and neutron stars (NSs), while the left exhibits potentialdiscoveries of intermediate-mass black holes (IMBHs) andintermediate mass-ratio inspirals (IMRIs). For reference, thecircle in the center represents the maximum reach of aLIGOat its design sensitivity [29].

controlled and isolated from the rest of the detector. Thecurvature of the Moon leads to a ∼450 m vertical offsetfor the light path between 40 km separation. An ideal sitefor GLOC would be within a bigger craters (& 20 km),providing a flat land for at least two end stations and ahigher elevation to place the third station.

The right panel of Fig. 1 shows the target sensitivity ofGLOC versus GW frequencies and compare it with otherproposed detectors [25, 30]. We consider two projectionsfor GLOC - a moderately ambitious approach to havedetection sensitivity down to flow = 0.25 Hz (GLOC-optimal), and a more conservative approach that reachesflow = 1 Hz (GLOC-conservative). The noise curves forGLOC can be downloaded from https://doi.org/10.

5281/zenodo.3948466.

In both the stated cases of GLOC, we assume that theprimary limiting noise in the mid to higher frequencieswill be dictated by the quantum noise. Below O(1)Hz,

the sensitivity of GLOC is governed by the seismicnoise and the suspension thermal noise. We expect theseismic noise in GLOC would be at least three ordersof magnitude lower than an ET-like configuration onEarth. Due to the Moon’s lower surface gravity, the noisefrom a suspension setup similar to that on earth wouldbe reduced by a factor of ∼3. Further improvementsin the thermal noise can be achieved by implementingmirror coating being planned for the cryogenic detector[31]. With these improvements, GLOC would achieve theprojected conservative sensitivity. To reach the optimalsensitivity will require an unconventional suspensionsetup. A possible mechanism it to let the test massesbe in a free fall with a so-called juggled interferometer[32]. Such a setup is more favorable to implement on theMoon due to the freedom with the atmospheric vacuum.

Methods.— For constructing the sensitivity curve ofGLOC, we apply the quantum noise in the range 2−5000Hz from the CE2-ifo available on pygwinc [33]. Toestimate the behavior of seismic and suspension noisebelow ∼ 2 Hz, we adapt their power-laws from the ET-D design and scale them to the improvement stated inthe concept design. We compute the horizon distance ofGLOC for various astrophysical binaries, characterizedby their masses (m1,m2), using the methods described inRef. [34]. For the space-based detectors, we set a timelineof 4 years. For the GW signal h(f), we utilize the stateof the art GW signal model IMRPhenomPHM [35]. Thismodel includes the radiated higher harmonics beyond thequadruple term that are crucial to probe intermediate-mass black hole binaries [36]. We set GLOC’s detectionthreshold at signal to noise ratio (SNR) of 8. The lowerlimit of integration for SNR is started from flow = 0.25Hz and includes a factor to account for the three detectorwithin GLOC’s triangular geometry. We transform theluminosity distance into redshift through Planck 2018Cosmology [28]. To estimate the sky-localization error∆Ω, we first compute the frequency bandwidth σf andtiming accuracy σt for a given astrophysical source [37].The effective baseline L is calculated through the orbitalpath of the Moon during the time spent by the GW signalin GLOC’s band. As the binaries spent most time atthe low-frequency regime of GLOC, we approximate theangular uncertainty as σθ ∼ σt(c/L) [38].

Science Case of GLOC.— As showcased with fig. 2,the detector would have a rare advantage of accessingGWs at cosmological distances across five orders ofmagnitude in mass - from sub-solar dark mattercandidates (∼10−1 M) [39] to stellar mass binaries(∼101−2 M) to intermediate-mass black holes (IMBHs,∼103−4 M) [40]. Across this entire mass-range, GLOC’ssensitivity would outperform that of the upcoming GWexperiments on Earth (CE, ET) and space (LISA) (seefig. 3). Furthermore, the sensitivity band of GLOC is notexpected to have any astrophysical foregrounds from the

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FIG. 3. High SNR detections. The area under each linerefers to the detection radius of equal-mass binaries at SNR≥ 100 for different GW detectors. The thick black (optimal)and grey (conservative) lines refer to sensitivity of GLOC. Thedashed lines refer to space-mission and colored lines indicatethe ground-based detectors discussed in this text.

white dwarf binaries [30]. Thus, any GWs with redshiftedfrequency fdet = (1 + z)fsrc & 0.2 Hz could be identifiedin the data without contamination.

At the detection threshold (SNR ≥ 8), we findthat GLOC can detect the mergers of neutron stars(NSs) and stellar black holes (BHs) to over 70% ofthe entire observable volume of our universe (z.100).This provides an unprecedented cosmological probe ofthe early universe, comparable to the 21 cm cosmologyproposed from the far-side of the Moon [41] andthe cosmic microwave background (CMB) experiments.While we do not expect stellar objects to exist beyondz∼70 [42], even one such detection will violate ΛCDMcosmology [43]. The measurements of stellar binariesat such high redshifts would also constrain the earlieststellar population [44].

With the low-frequency limit up to ∼0.2 Hz, GLOCwill start detecting the inspiral of stellar binaries a fewmonths to days before their merger [45]. This makesGLOC an early alert system for all coalescing GWsources in the Earth-based network. Unlike other deci-Hz proposals (such as DECIGO), GLOC would continueto measure the binary all the way up to merger andringdown. This ensures that for stellar binaries, (i) thedetection radius in in GLOC is comparable (or better)to the most futuristic concepts proposed for space-baseddetectors, (ii) the overall SNR in GLOC is about an

order of magnitude higher than next-generation Earth-based detectors on Earth, and (ii) the effective baselineL of GLOC would become comparable to the Moon’sorbital diameter around the Earth. While this study setsthe high-frequency sensitivity of GLOC (& 100 Hz) tobe comparable to CE, this can be traded for a lower-cost design as most SNR is accumulated with the low-frequency improvements.

The typical SNRs in GLOC for stellar binaries fromhigh redshifts (z ∼ 3−10) would be∼100, thus the timingaccuracy, σt, could be as good as ∼0.1 milli-seconds [37].This combined with the motion of the Moon at ∼1 km/swill reduce the angular uncertainty to σθ ∼ 10−3 deg.As a result, the sky-localization of stellar binaries fromGLOC alone will be ∆Ω ∼ 10−5 deg2. In Fig. 4, weshow this approximate constraint on sky-localization forcoalescing binaries at different redshifts.

A binary neutron star (BNS) at z ∼ 2 would be in theGLOC band for an entire orbital period of the Moon,while a nearby BNS (like GW170817 [46]) would be in-band for almost three months. The sky-localization alertfor BNSs can be sent days in advance, allowing readinessof high-latency electromagnetic followups with reach upto high redshifts. Even in the case of GLOC-conservative,the effective baseline for a BNS would be a quarter of theMoon’s orbit, leading to tight constraints.

For a relatively light binary black hole (BBH) likeGW151226 [47], GLOC would start measuring its inspirala day before the merger. These could constrain thesources at redshifts ∼2 to about 0.1 arcmin2. Nextgeneration Earth-based detectors CE and ET have theirpeak sensitivity for BBHs of these total masses [34].A combined network between these enhanced detectorson Earth and a geocentric detector like GLOC canfurther reduce the sky-location error by two ordersof magnitude (see calculations in [48]). As shownin Fig. 4 (dotted line), these combined network canconstrain mergers of light BBHs to 1 arcsec2, namely theangular scale of a single galaxy. These are the tightestconstraints on the source location in GW astronomy,allowing to identify the potential host galaxy withoutelectromagnetic counterparts [49–52]. The strongestscience case of GLOC is opening such high redshift darksirens to independently measure the evolution of theHubble parameter as a function of redshift [53].

For the emerging population of BBHs in the pair-instability supernovae (PISN) mass-gap [54], such asGW190521 [55, 56] and GW170502 [57], GLOC wouldmeasure their inspiral a few hours before their mergers.These are the brightest sources in GLOC, registeringSNR ∼ 100 at z . 20. For comparison, a deci-Hzspace-mission like DO would have similar reach only upto z . 1, while ET it can reach z . 10 (see fig. 3).A multiband observation between GLOC and ET wouldconstrain the sky-location to ∼1 arcmin2, proving criticalfor associating flares in Active Galactic Nuclei (AGN)

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FIG. 4. Sky-localization with GLOC. Each colored codedcurve represents a face-on binary at different redshifts. Thehighlighted masses are in the source frame of the binary. Theshaded region refers to the potential improvement for a 10 +10 M binary with multiband network on GLOC (optimal)and next-generation Earth-based detectors.

with such binaries [58]. Furthermore, the inclinationangle and orbital eccentricity will be tighter constrainedby measuring the early inspiral in GLOC, thus reducingthe error in redshift and the corresponding source-framemass of black holes. The constraints on the secondaryblack hole will be particularly important in probing thelower-end of the PISN mass-gap. While a space-missionlike LISA can measure the early-inspiral of these PISNBBHs years in advance [59], it can only do so for sourcestypically within a Gpc [34] and retrospective after adetection from Earth [60].

The enhanced low-frequency sensitivity permits GLOCto survey binaries with IMBHs of 102−4 M, practicallyacross the entire universe. Such cosmological reach iscrucial for connecting IMBHs with the Pop-III remnants[61] and the seeds of super-massive black holes [62–64]. The theoretical estimates on their populationsare fairly weak, but the upper-limits from LIGO andVirgo detectors [65] suggests that the mergers of lower-range IMBH binaries are much rarer (. 1 Gpc−3 yr−1)compared to stellar binaries. Unlike GLOC, space-missions have just a few years of lifetime (4−10 years forLISA), allowing the detection of only a handful of such

rare sources.

In the case of potential IMBH detection, the advent ofGLOC opens a new possibility of multiband observationsacross three frequency bands - from early inspiral atmilli-Hz (space), to late-inspiral at deci-Hz (Moon)and mergers/ringdown at ∼10 Hz (Earth). Suchjoint measurements of a source across three bands offrequency spectrum would provide the strongest testsof the black hole area theorem, and no-hair theorem[10, 66, 67]. The morphology of gravitational-waves inmultiband of LISA and GLOC could provide a directprobe of the environment surrounding these black holes[68]. Furthermore, the intermediate-mass-ratio inspirals(IMRIs) [69], which are relatively weak sources in bothLISA and the next-generation Earth detectors, can besurveyed in GLOC to z ∼ 10. For IMRIs within redshift. 1, GLOC would measure them with SNR ∼ 100. Thiswould increase the detection confidence of these sourcesin LISA and ET, thus improving their overall parameterestimation.

The long-term detection sensitivity at O(1 Hz) isunique to GLOC. This frequency regime is crucial forprobing the explosion mechanism of Type Ia supernovae(SNe) [9]. For the the single degenerate channel of TypeIa, we expect the GW emission at around 1 Hz [70, 71]. Ifthe progenitors of Type Ia SNe are mergers of two whitedwarfs (double degenerate channel), we expect GLOCto detect them up to ∼2 Gpc. These detections willalso tightly bound the unknown masses of the whitedwarfs, thus reducing the error budget in calibrating thestandard candles.

At the low end of source masses, GLOC can putthe tightest bounds on a putative population of sub-solar dark matter objects (0.1 − 1M) [39]. Thereare no known astrophysical phenomena that can createdetectable GWs at such low-masses, however, primordialblack holes or dark matter within neutron star cores offerpossible scenarios (see [72] and references within). Thelow-frequency sensitivity of GLOC allows us to measurethe dark matter density of such exotic objects to 30% ofthe entire observable volume of the universe (z ∼ 10).

Acknowledgements.— We are grateful to Rainer Weiss,Stavros Katsanevas, Scott Hughes, Mathew Evans, BobEisenstein, Kevin Kuns, Brian O’Reilly, Stefan Hild,Kelly Holley-Bockelmann, Jan Harms, Szabolcs Marka,Philippe Lognonne, Robin Stebbins, Peter Bender,Robert Fisher and the referees for insightful comments.K.J’s research was supported by the GRAVITY programat Vanderbilt University. A. L.’s work was supportedin part by the Black Hole Initiative at HarvardUniversity, which is funded by grants from the JohnTempleton Foundation and the Gordon and Betty MooreFoundation.

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