Introduction

The past five years have witnessed a revolution in astronomy. The direct detection of gravitational waves (GW) emitted from the binary black hole (BBH) merger GW150914 (Fig. 1) by the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detector1 on September 14, 2015 (ref.2) was a watershed event, not only in demonstrating that GWs could be directly detected but more fundamentally in revealing new insights into these exotic objects and the Universe itself. On August 17, 2017, the Advanced LIGO and Advanced Virgo3 detectors jointly detected GW170817, the merger of a binary neutron star (BNS) system4, an equally momentous event leading to the observation of electromagnetic (EM) radiation emitted across the entire spectrum through one of the most intense astronomical observing campaigns ever undertaken5.

Fig. 1: The detected gravitational-wave strain amplitude as a function of time for GW150914, the first signal detected nearly simultaneously by the LIGO Hanford and Livingston observatories on September 14, 2015.
figure 1

The waveforms are shifted and inverted to compensate for the slightly different arrival times and different orientations of the detectors (red: LIGO Hanford, blue: LIGO Livingston). The upper inset is a simulation of the merger produced using numerical relativity to illustrate the evolution of the black hole event horizons as the system coalesces and merges. Figure adapted with permission from ref.2, CC BY 3.0 (https://creativecommons.org/licenses/by/3.0/).

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Coming nearly 100 years after Albert Einstein first predicted their existence6, but doubted that they could ever be measured, the first direct GW detections have undoubtedly opened a new window on the Universe. The scientific insights emerging from these detections have already revolutionized multiple domains of physics and astrophysics, yet, they are ‘the tip of the iceberg’, representing only a small fraction of the future potential of GW astronomy. As is the case for the Universe seen through EM waves, different classes of astrophysical sources emit GWs across a broad spectrum ranging over more than 20 orders of magnitude, and require different detectors for the range of frequencies of interest (Fig. 2).

Fig. 2: The gravitational-wave spectrum probed by strain-sensitive gravitational-wave detectors, ranging from 10−9 Hz to more than 1,000 Hz.
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The source classes are shown above the spectrum and the detectors below. The portion of the gravitational-wave spectrum below 10−9 Hz probed through measurements of the cosmic microwave background polarization is not shown.

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In this Roadmap, we present the perspectives of the Gravitational Wave International Committee (GWIC, https://gwic.ligo.org) on the emerging field of GW astronomy and physics in the coming decades. The GWIC was formed in 1997 to facilitate international collaboration and cooperation in the construction, operation and use of the major GW detection facilities worldwide. Its primary goals are: to promote international cooperation in all phases of construction and scientific exploitation of GW detectors, to coordinate and support long-range planning for new instruments or existing instrument upgrades, and to promote the development of GW detection as an astronomical tool, exploiting especially the potential for multi-messenger astrophysics. Our intention in this Roadmap is to present a survey of the science opportunities and to highlight the future detectors that will be needed to realize those opportunities. The recent remarkable discoveries in GW astronomy have spurred the GWIC to re-examine and update the GWIC roadmap originally published a decade ago7.

We first present an overview of GWs, the methods used to detect them and some scientific highlights from the past five years. Next, we provide a detailed survey of some of the outstanding scientific questions that can be answered with planned or envisioned future GW detectors. We then discuss the future prospects for synergistic observations using GW and EM observatories. Finally, we highlight some of the technological challenges to be overcome to build future GW detectors before concluding.

GW fundamentals and detectors

Fundamentally different from and complementary to other astrophysical ‘messengers’ such as photons, neutrinos or cosmic rays, GWs provide unique information about the most energetic astrophysical processes in the Universe by carrying information about the dynamics of massive objects such as black holes and neutron stars moving at relativistic speeds. As predicted by general relativity (GR), GWs are transverse (oscillating perpendicular to the direction of propagation), travel at the speed of light and possess two polarizations.

GWs physically manifest themselves as time-dependent strains, h, in spacetime, or, more precisely, h = δL/L, where L is the distance between two reference points in space and δL is the induced displacement over the baseline L. GR predicts that the induced strain is perpendicular to the axis of GW propagation and is quadrupolar, that is, a wave travelling along the z-axis stretches (then compresses) the path along the x-axis while shrinking (then stretching) the y-axis (for one polarization; in the orthogonal polarization, the elongation/compression occurs along axes rotated 45° relative to the x-axis and y-axis). GW detectors rely on a measurement of the variations in the light travel time between separated reference points — or ‘test masses’ — caused by a passing GW. The test masses are configured such that each is in near-perfect free fall (and, as such, approximate a local inertial frame) and are separated over very long baselines. The light travel times between pairs of test masses are monitored and read out via a detector such that any changes in the spacetime curvature caused by passing GWs induce modulations in these light travel times. This concept is simply illustrated for ground-based detectors in Fig. 3, which shows a simple Michelson interferometer.

Fig. 3: The concept of a simple laser interferometer gravitational-wave detector.
figure 3

A gravitational-wave (GW) strain shortens one arm while lengthening the other as it passes the detector, resulting in a slight difference in round-trip travel time for the laser light. This, in turn, leads to a phase shift of the light in one arm of the detector relative to the other, creating a change in light intensity at the photodetector. The time-dependent intensity recorded by the photodetector produces a reconstruction of the propagating GW.

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Ground-based detectors

Current ground-based observatories probe the high-frequency portion of the GW spectrum from ~10 Hz to ~10 kHz dominated by stellar-mass compact sources, such as coalescing BBH and neutron star systems, and (as yet to be observed) supernovae and isolated neutron stars. All ground-based detectors use enhanced Michelson interferometry with suspended mirrors to directly measure a GW’s phase and amplitude. The detection of audio-band GWs places extremely stringent demands on the isolation of the mirrors from local forces and disturbances. The two US-based Advanced LIGO detectors1 have L = 4 km arm lengths, whereas the European-based Advanced Virgo3 and the Japan-based KAGRA8,9 have L = 3 km arms. Typical strains from astrophysical sources are on the order of 10−21 or less, thus, displacement sensitivities δL of less than ~10−18 m are required to detect GWs with sufficient signal-to-noise (SNR) ratio. This is an incredibly small displacement; for comparative purposes, note that the radius of a proton is ~8.5 × 10−16 m.

A schematic view of Advanced LIGO, shown in Fig. 4, illustrates the configuration of the current generation of ground-based detectors. The mirrors are suspended from multi-stage pendulum systems such that, above the resonant frequencies of the suspension system (typically around 1 Hz), they can be effectively treated as in free fall (that is, in a local inertial frame) in the direction of light propagation. These suspensions and accompanying seismic isolation systems reduce the undesired test-mass motion induced by ambient ground motion by about a factor of 1012 from 1 Hz to 10 Hz (refs3,10). In addition to seismic noise, there are three primary noise sources that currently limit interferometer sensitivity: thermal noise produced by random displacements of the mirror surfaces that are produced by thermally fluctuating stresses in the mirror coatings, substrates and suspensions11; Newtonian (or dynamic gravity gradient) noise arising from earth (ground) and atmospheric density perturbations directly exerting dynamic forces on the mirrors12; and quantum noise resulting from both vacuum fluctuations of the EM field that limit phase resolution in the readout photodetector (so-called ‘shot noise’) and displacements of the mirrors via quantum radiation pressure noise (QRPN), which induce stochastic impulses (or ‘kicks’) on the mirrors due to the random arrival time of the momentum-carrying photons13.

Fig. 4: A schematic of a working laser interferometer gravitational-wave detector.
figure 4

a | A simplified view of the Advanced LIGO interferometer, showing the optical configuration including the laser, input mode cleaner, power-recycling and signal-recycling cavities, the 4-km-long arm cavities and the output mode cleaner. The gravitational-wave (GW) signal is recorded on the output photodiode after the output mode cleaner. b | A schematic of one of the arm cavities. The input test mass (ITM) and end test mass (ETM) mirrors are held by quadruple suspensions to suppress ground motion disturbances. Panel a courtesy of LIGO/Fabrice Matichard. Panel b courtesy of LIGO/Daniel Sigg.

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The effect of QRPN is diminished as the mirror mass increases, and both QRPN and shot noise can be reduced by injecting quantum-engineered squeezed vacuum states of light into the interferometer14. Thermal noise manifests itself in a variety of ways in mirror coatings, mirror substrates and suspensions15; it can be understood from a statistical mechanics perspective as infinitesimal internal motions of macroscopic objects at non-zero temperatures caused by intrinsic dissipation (or mechanical loss) in the system. In addition to these fundamental noise sources, a very large number of technical noises must be identified and overcome, which broadly group into laser frequency and intensity noises, acoustically and seismically driven scattered light noises, sensor and actuator noises, stochastic forces from electrical and magnetic fields, and, potentially, energy deposited by energetic particles. (More details about these noise sources are presented in the last section, where we discuss some of the challenges to building future ground-based detectors.)

To deliver the best science, a network of globally distributed interferometers functioning as a unified detector is required. The Advanced LIGO and Advanced Virgo detectors have actively searched the GW sky in a highly coordinated campaign during a series of observing runs carried out from 2015. Figure 5 shows the sensitivities of the LIGO and Virgo interferometers during the ‘O2’ observing run; in the latest ‘O3’ run, the detectors have achieved sensitivities sufficient to detect BBH mergers on a weekly basis16.

Fig. 5: The sensitivity of the LIGO-Virgo network for the ‘O2’ observing run plotted as a function of frequency.
figure 5

The vertical axis presents the sensitivity as an amplitude spectral density, that is, the strain per unit square root of frequency. The stable, narrow spectral features are due to very high-Q mechanical resonances and electrical (50-Hz or 60-Hz) coupling. At low frequencies, scattered light, seismic and control noise dominate; in the mid-band, thermal noise in the mirror dielectric coatings is the leading term. At high frequencies, quantum noise is the limit to sensitivity. Figure adapted with permission from ref.26, CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).

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The KAGRA detector recently joined LIGO and Virgo to form the LIGO-Virgo-KAGRA network; the LIGO-India17 interferometer will be joining later in this decade, dramatically improving the ability of the network to confidently detect and locate GW events18 and providing new methods for testing alternative theories of gravity through enhanced ability to resolve GW polarizations19.

The LIGO-Virgo observations have, in a few years, already produced revelations about some of the most energetic and cataclysmic processes in the Universe. From GW150914, and more recent BBH mergers observed by the LIGO Scientific and Virgo collaborations, it is now known that there is a population of black holes paired in orbitally bound binary systems that evolve through the emission of GWs and merge in less than a Hubble time (the age of the Universe); that black holes of many tens and even hundreds of solar masses exist in nature; and that the properties of the observed black holes are entirely consistent with GR to within current measurement limits16,20,21,22,23,24,25,26,27,28. The BNS detection GW170817 and subsequent observations in the EM domain collectively comprise the first demonstration of GW–EM multi-messenger astronomy, providing an astounding wealth of knowledge, including the first definitive link between BNS merger progenitors and short gamma-ray bursts29,30,31,32,33,34,35,36,37; the first definitive observation of a kilonova38,39,40,41,42,43,44,45,46, conclusive spectroscopic proof that BNS mergers produce heavy elements through r-process nucleosynthesis40,47,48,49,50,51,52; the first demonstration that GWs travel at the same speed as light to better than a few parts in 1015 (ref.29); and an independent method for measuring the Hubble constant using detected GWs as a ‘standard siren’ for determining the absolute distance to the source53,54,55. Additionally, the Advanced LIGO and Advanced Virgo detections have enabled tests of GR in the strong gravity regime that were inaccessible to other experiments and astronomical observations56,57, motivating research on many fronts in fundamental physics and astrophysics. This only represents a brief overview of the recent discoveries and, as we discuss in detail below, captures only a fraction of the potential science afforded by future GW observations.

Space-based detectors

When launched in the mid-2030s, the Laser Interferometer Space Antenna (LISA)58 will possess a breathtaking scientific portfolio. LISA will explore much of the GW Universe in the frequency band from 100 μHz to 100 mHz. A constellation of three satellites separated by 2.5 × 109 m in an Earth-trailing orbit, LISA will be capable of detecting the first seed black holes formed out to redshifts z ~ 20 or more59, and intermediate-mass and ‘light’ super-massive coalescing black hole systems in the 102–107 M⊙ (solar mass) range, thus, tracing the evolution of black holes from the early Universe through the peak of the star formation era. Through detections of extreme mass ratio inspirals (EMRIs, binary systems with mass ratios as small as ~10−6)60, LISA will directly map the curvature of spacetime at the event horizons of massive black holes, yielding even more precise tests of GR in the strong gravitational field regime. LISA might also detect stellar-mass BBH systems years before they are detectable by ground-based detectors61, and provide very precise sky localization of such events for EM follow-up. By discovering new sources of galactic compact binaries comprised of white dwarfs, neutron stars and stellar-mass black holes, LISA will survey the predominant population of binary compact objects and map the structure of the Milky Way62.

The LISA Pathfinder (LPF)63, launched in 2015 and operated until mid-2017, has paved much of the way for the full-scale LISA mission. LPF was a European Space Agency (ESA) mission, with contributions from a consortium of European national agencies, as well as NASA. It convincingly demonstrated some of the key performance requirements for the full LISA mission, most notably the displacement sensitivity and control of spurious acceleration noise required for LISA. More on LISA science is presented in the next section, whereas the LISA and LPF detector technology is discussed in detail in the last section.

PTAs

Pulsar timing arrays (PTAs)64,65,66,67 explore the nanohertz portion of the GW spectrum ranging from 10−9 to 10−6 Hz. Rather than using laser light to measure variations in detector length as ground-based and space-based detectors do, a PTA measures variations in the radio frequency pulse arrival times at the Earth from an array of millisecond pulsars68,69 (Fig. 6).

Fig. 6: Illustration of the radio pulsar timing process.
figure 6

The pulsar beams sweep across the radio antenna and are detected using a radio receiver at ~GHz frequencies. The data are corrected for delays due to the interstellar medium (‘de-dispersion’) and then folded at the period of the pulsar to create an integrated profile. This profile is then cross-correlated with a noise-free template profile to calculate a time of arrival (TOA), using a high-precision reference clock at the observatory.

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Pulsars are rotating neutron stars that act like cosmic lighthouses, appearing as periodic pulsating radio sources. Because millisecond pulsars, pulsars with periods between roughly 1.4 and 30 ms, possess rotational stabilities comparable with the best atomic clocks, they are ideal timing sources. Once effects such as rotational spin-down, astrometric position and motion, and orbital effects from binary companions are accounted for, the pulse arrival times can be precisely modelled and predicted to fractions of a microsecond for up to decades into the future70, and variations arising from GW perturbations can be measured. Distortions in the spacetime around Earth or the pulsars will produce systematics in timing residuals (deviations of the measured pulse arrival times relative to the predicted arrival times), and, crucially, spatially correlated systematics in the timing residuals of the array of pulsars across the sky71. A GW emitted from a single binary system passing the pulsar-Earth system will cause two frequency components in the time series of the timing residuals: one from the spacetime variations at the pulsar (‘pulsar term’), the other from variations at the Earth (‘Earth term’), with different frequencies resulting from changes in the orbital frequency of the emitting source during the time it takes for the radio pulses to travel to the Earth. The top panel of Fig. 7 shows the expected detection in the form of the Hellings and Downs curve, the correlated response of a pair of pulsar-Earth baselines to a stochastic GW background averaged over all sky positions and polarizations as a function of the angle between the pulsar pair-Earth baselines71.

Fig. 7: The pulsar timing array network.
figure 7

The top plot represents the Hellings and Downs curve, showing the predicted correlation in pulsar timing residuals as a function of millisecond pulsar angular separation resulting from a stochastic gravitational-wave background. The lower map shows the telescopes that have been or will in the future be used for this experiment. Arecibo (Puerto Rico), the Green Bank Telescope (GBT; West Virginia), Lovell (UK), Effelsberg (Germany), Nançay (France), Westerbork Synthesis Radio Telescope (WSRT; Netherlands), Sardinia Radio Telescope (SRT; Italy) and Parkes (Australia) are currently contributing International Pulsar Timing Array (IPTA) data. The Very Large Array (VLA; New Mexico) will soon begin to contribute. The Deep Space Station 43 (DSS-43; Australia), the Molonglo Observatory Synthesis Telescope (MOST; Australia), the Giant Metrewave Radio Telescope (GMRT; India) and Ooty (India), as well as three under-construction telescopes — CHIME (Canada), Five-hundred-meter Aperture Spherical Telescope (FAST; China) and MeerKAT (South Africa). Figure courtesy of Shami Chatterjee.

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Pulsars are observed at monthly or more rapid cadences in order to sample and measure changing properties, such as the position of the pulsar (that is, proper motion) and varying dispersion due to the interstellar medium. In addition, they must be observed for roughly one half-hour per observation to average over enough of the pulses to mitigate the effects of jitter induced by astrophysical and receiver noise. The observations themselves cover very wide bandwidths (>GHz) or occur near-simultaneously at multiple radio frequencies in order to correct for the effects of interstellar dispersion. Pulsar timing instruments must have fine frequency resolution (~1 MHz) to correct for these effects, coupled with high time resolution in order to sufficiently sample the roughly millisecond-wide radio pulses.

As each pulsar needs to be timed for about a year (equivalent to one Earth orbit) to be properly localized and understood, PTA experiments must have years-long durations. In practice, the lower end of the frequency window is given by the length of the data set (currently about 1 nHz), whereas the upper end is given by the cadence of the timing observations (currently about 1 μHz). Timing residual amplitudes of about 100 ns or less are resolved for the best timed millisecond pulsars.

Today, there are three major PTAs: the Parkes PTA72 in Australia, the European PTA Consortium65 and the NANOGrav73 consortium in North America. These arrays regularly achieve sub-microsecond timing on over 100 millisecond pulsars (MSPs), which collectively form the International Pulsar Timing Array74 (IPTA). PTA science is often sensitivity-limited, and many of the MSPs being discovered in recent surveys have flux densities that often require hour-long observations with 100-m class (or larger) telescopes to achieve the requisite sub-microsecond timing. The Five-hundred-meter Aperture Spherical Telescope (FAST) (500 m diameter) and MeerKAT (64 antennas × 13.7 m diameter) telescopes have been commissioned, and are now commencing regular MSP timing, joining many existing 64–100-m class facilities in the Northern Hemisphere, and the Parkes 64-m telescope in the Southern Hemisphere. Figure 7 illustrates the radio telescopes used for pulsar timing experiments around the globe. NANOGrav has used two telescopes — the Arecibo Observatory (AO) in Puerto Rico and the Green Bank Telescope (GBT) in West Virginia — with each telescope providing roughly half of the sensitivity to GWs. NANOGrav currently observes almost 80 MSPs, about half at the AO and the other half at the GBT, and is seeing the first indications of a signal consistent with GWs75.

The recent loss of the AO poses significant challenges. In the short term, to minimize the loss of sensitivity to the stochastic background of GWs, NANOGrav is going to move most of the pulsars observed at the AO to the GBT, requiring roughly double the amount of time currently used at the GBT. Longer term, the US community will need a replacement for the AO (such as the DSA-2000 concept76). Legacy AO observations will anchor combined future data sets, allowing us to characterize the low-frequency GW universe and glean unique insights into galaxy evolution and cosmology.

The most promising GW sources in the nanohertz band are super-massive (107–1010 M⊙) binary black holes (SMBBHs) that form via the collisions of massive galaxies. The astrophysical stochastic gravitational-wave background (ASGWB) produced by the cosmic population of slowly inspiralling SMBBHs across the Universe77,78,79 is the first signal likely to be detected, due to the very long lifetime in the detection band and the relatively small rate of systems in the final coalescence phase. As sensitivity improves, this may be followed by the observation of individual SMBBHs80,81,82; parallel EM observations can both help recover GW signals and allow for richer physics to be extracted. The detection of the ASGWB will reveal essential information about the formation of the large-scale structure of the Universe, determine the rates of galaxy mergers and definitively resolve the ‘final parsec’ problem83 — the theoretical difficulty of shrinking the orbit of a SMBBH by a factor of ~100 after its formation at a separation of ~1 pc via the scattering of stars. PTA measurements are currently probing the expected range of astrophysical signals84,85,86,87 and, based on recent results, a detection of the ASGWB may be imminent79. The detection of individual SMBBHs will allow for combined EM and GW multi-messenger observations and, although only a handful are expected, the scientific return of these discoveries will be immense88.

Cosmic microwave background polarization

The lowest frequencies of the GW spectrum, down to approximately 10−18 Hz, are populated by a stochastic background of remnant primordial GWs produced during the Big Bang. Standard inflationary cosmology predicts a GW spectrum too feeble to be detectable by current ground-based detectors, LISA or PTAs, although some extensions of inflation and more exotic models, including first-order phase transitions and topological defects, predict primordial GW energy densities that can be detected across the frequency bands89,90. EM-based measurements of the cosmic microwave background (CMB) polarization may reveal signs of the remnant primordial GWs91. As CMB polarization measurements are based on a fundamentally different detection method than their higher frequency counterparts, this approach is not discussed further here.

Upcoming physics and astronomy with GWs

In the coming decades, the new observational window of GW astronomy promises to deliver data that will transform the landscape of physics, addressing some of the most pressing problems in fundamental physics, astrophysics and cosmology88,92,93,94,95 (see Box 1). The next generation of ground-based GW observatories planned for the 2030s, the Einstein Telescope (ET, ref.96) and Cosmic Explorer (CE, ref.97) (collectively referred to as 3G), as well as the LISA58 mission, will observe merging black holes and neutron stars when the Universe was still in its infancy. PTAs (ref.74) will continue to evolve to greater sensitivity. LIGO Voyager98, a major upgrade under consideration for the current LIGO observatories in the late 2020s, could test some of the key technologies needed for the ET and CE and, at the same time, provide a significant increase in sensitivity over the current generation of detectors. With all of these instruments, one can expect to witness extremely high SNR events that could reveal subtle signatures of new physics. The potential of GW science in the next two decades is illustrated in Fig. 8, which compares the reach of the current ground-based detectors Advanced LIGO and Advanced Virgo with that of planned 3G observatories for 1.4–1.4 M⊙ BNS and 30–30 M⊙ BBH mergers as a function of redshift and ‘lookback’ time towards the Big Bang.

Fig. 8: The conceptual reach of next-generation, ground-based detectors.
figure 8

Shown is the range of the current ground-based detectors and future planned detectors Einstein Telescope (ET) and Cosmic Explorer (CE) to detect 1.4 + 1.4 solar mass (M⊙) binary neutron star (BNS) (left) and 30 + 30 M⊙ binary black hole (BBH) (right) mergers as a function of ‘lookback’ time (to the Big Bang) and redshift. Yellow (white) circles represent populations of BNS (BBH) mergers as a function of redshift or lookback time. CE is envisioned to be implemented in two phases, designated CE1 and CE2. At their ultimate planned sensitivities, ET and CE will be able to observe all stellar-mass BNS and BBH mergers. BH, black hole; NS, neutron star. A+ refers to Advanced LIGO and O3 to the third LIGO-Virgo operating run. Figure courtesy of Evan Hall.

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Fundamental physics

GW observations, because they explore the most extreme conditions of spacetime and of matter, can serve as unsurpassed probes of fundamental physics. In this section, we will look at the power of this new tool in exploring gravity and matter at their most extremes.

Testing GR and modified theories of gravity

GR has been a tremendously successful theory in explaining current astronomical observations and laboratory experiments99,100,101. Nevertheless, there is a general consensus that GR is, at best, incomplete, representing an approximation to a more complete theory that cures some or all of its problems102. These issues include the loss of information down a black hole103, which contradicts unitary evolution of physical states in quantum mechanics; the inevitability of spacetime singularities104,105, for example, at the centre of a black hole where physical quantities such as the density and curvature of spacetime become infinitely large; a cosmological constant that is responsible for the late-time accelerated expansion of the Universe106,107, whose value cannot be accounted for in the standard model of particle physics108; and the lack of a viable formulation of quantum gravity, which might resolve all of these problems but has, so far, been elusive. These difficulties led to increased interest in searching for GR violations in observations in the hope that they will provide clues to an alternative theory of gravity.

The spacetime curvature at the horizon of a black hole of mass M and radius R ~ 2GM/c2 goes as \(\kappa \sim \sqrt{GM\,/\,{c}^{2}{R}^{3}}={c}^{2}\,/\,\sqrt{8}GM\), where G is the gravitational constant and c is the speed of light. Note that κ is larger for lighter black holes, thus, binary coalescences of the lightest astrophysical black holes are, therefore, the strongest regions of gravity that we know of and are ideal for testing strong field predictions of GR101,102. Sub-solar-mass black hole binaries, should they exist, would have even greater curvature. Although neutron stars are lighter than astrophysical black holes, they are not as compact and, hence, probe smaller curvature scales. Black holes also probe regions of greatest compactness (or dimensionless gravitational potential) defined as Φ = GM/c2R, which is largest for black holes. Past experiments such as the Cassini spacecraft109 and the double pulsar orbital decay110 verified the validity of GR in regimes where fields are moderately strong and/or velocities are small compared with the speed of light (see Fig. 9). Current and future experiments, such as the Event Horizon Telescope (EHT)111 and the GRAVITY instrument112, explore the validity of GR near massive black holes and, hence, in the small curvature, but high compactness, regime. X-ray observations by the NICER experiment113 probes GR in the high curvature and large compactness regime of neutron stars114, whereas GW observations of stellar-mass black holes by ground-based detectors (area denoted by ‘GW ground’ in Fig. 9) and LISA probe regions’ curvature and compactness on a wide range of scales: stellar-mass black holes of up to ~5–100 M⊙ (mostly ground-based observatories, but also LISA for sources that are close by), intermediate-mass black holes of 102–104 M⊙ (ground-based observatories and LISA) and super-massive black holes (SMBHs) of 105–1010 M⊙ (LISA at the lower end and PTAs at the higher end of the mass range), offering tests of GR over ten orders of magnitude in length scale and twenty orders of magnitude in curvature.

Fig. 9: Gravitational-wave observations offer a unique ability to test general relativity in regions of high curvature and strong gravity.
figure 9

The plot shows the curvature scale κ (in km−1) due to the presence of mass M of size R defined as \(\kappa \equiv \sqrt{GM\,/\,{c}^{2}{R}^{3}}\), where G is the gravitational constant, and the compactness, or the dimensionless gravitational potential, Φ ≡ GM/c2R probed by different experiments. For example, observation of the double binary pulsar (total mass of 2.6 solar masses (M⊙) and orbital separation of ~106 km) probes the curvature scale of κ ~ 2 × 10−9 km−1 and compactness of Φ ~ 4 × 10−6. In contrast, a black hole binary of total mass 10 M⊙ at the time of merger probes a curvature scale of κ ~ 2.4 × 10−2 km−1 and compactness of Φ ~ 0.5. Filled circles represent past experiments that have verified general relativity at the corresponding curvature scale and compactness. Rectangles and the rhombus represent ongoing or future experiments that will probe ever greater scales of curvature and compactness. (LAGEOS stands for the Laser Geometric Environmental Observation Survey; NICER stands for Neutron star Interior Composition Explorer; EHT stands for Event Horizon Telescope and is represented by the blue vertical rectangle; S2 and IR Flare refer to monitoring of the star ‘S2’ and near-infrared flaring near Sagittarius A*; GW ground indicates gravitational-wave observations by ground-based detectors.) Figure adapted with permission from ref.256, APS.

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In addition to probing the strong field predictions of GR, the vast cosmological distances over which GWs travel (redshifts in excess of z ~ 20 both in the case of LISA and future ground-based detectors) will greatly constrain local Lorentz invariance and graviton mass99. Violations of Lorentz invariance or a non-zero graviton mass could cause dispersion in the observed waves and, hence, help to discover new physics predicted by certain quantum gravity theories. At the same time, propagation effects could also reveal the presence of large extra spatial dimensions that lead to different values for the luminosity distance to a source inferred by GW and EM observations (see refs115,116) or cause birefringence of the waves predicted in certain formulations of string theory, as discussed in refs117,118. In certain modified gravity theories, GWs have more than two polarizations (in contradiction with GR); the presence of such additional degrees of freedom could be explored by future detector networks99,152), EMRIs at z ≲ 1 (ref.153) and SMBBHs up to z ≈ 10 (ref.154) will enable precision cosmology across the entire astrophysically relevant redshift range.

With a population of compact binary mergers observed with 3G detectors, and their redshifts obtained by follow-up EM observations, it will be possible to accurately measure cosmological parameters such as the dark matter and dark energy densities, and the equation of state of dark energy155, giving a completely independent and complementary measurement of the dynamics of the Universe.

Astrophysical and primordial stochastic backgrounds

The ASGWB that will be detected by PTAs also contains cosmological information. The properties of the ASGWB depend on the formation and evolution of cosmological source populations86. PTA measurements of the ASGWB produced by SMBBHs, the most promising GW source in that band, will constrain the evolution of the SMBHs that become quasi-stellar objects and active galactic nuclei (AGN). In addition, PTAs are sensitive to GWs produced by fundamental physical phenomena such as phase transitions in the early Universe, cosmic strings and inflation, all of which would provide unique windows into high-energy and early-Universe physics156,157,164 of the stochastic GW background produced by the most massive black hole binaries in the Universe. EMRIs can probe the population of inactive (thus, otherwise invisible) SMBHs, providing invaluable insights into the low-mass end of the SMBH mass function down to the mass scales of dwarf galaxies. The properties of individual inspirals (such as eccentricity and orbital inclination) carry information on the dynamical processes governing the evolution of dense relativistic systems, offering a unique laboratory for testing strong gravity.

At the super-massive end of the mass spectrum, PTAs are expected to reveal the cosmic population of inspiralling SMBBHs that inhabit the largest galaxies in the Universe82,164. These objects are in a frequency range inaccessible to LISA and ground-based detectors. Outstanding questions such as the precise occupation fraction of SMBHs in galaxies, the merger rate of galaxies, the relation between galaxy masses and the masses of the SMBHs they host, the efficiency of pairing of SMBHs and the nature of their dynamical interaction with the environments at the cores of galaxies will be answered by deciphering the information encoded in the amplitude and shape of the ASGWB spectrum88. The detection of the ASGWB will definitively resolve the ‘final parsec’ problem, proving that SMBHs can merge and possibly elucidating their dynamical interactions in the cores of galaxies. The dominant dynamical processes are expected to be the scattering of stars on orbits that intersect the galactic core or interactions with a circumbinary disk. PTAs probe frequencies at the interface between the environment-driven regimes (when the SMBHs are far apart) and GW-dominated regimes (when the SMBHs separations are below a milliparsec). Each dynamical mechanism also predicts different inspiral timescales compared with estimates that assume GW-driven inspiral, so measuring the ASGWB spectrum can provide clear evidence of which dynamical processes dominate in these massive galaxy hosts. Individual SMBBH systems are expected to be detected after the detection of the ASGWB. Studies of individual systems, coupled with EM observations, will allow probing the astrophysical processes driving mergers even further, and determine how the importance of various processes depends on the properties of the galaxies88.

Multi-messenger astronomy with GWs

Dawn of a new multi-messenger era

The detection of GWs from the inspiral and merger of the first BNS system GW170817 (ref.4) marked the start of an era of multi-messenger astronomy incorporating GW observations5. The extensive multi-wavelength, multi-year follow-up campaign of GW170817 enabled the detection of counterparts in almost all the EM bands, confirming that the merger of a binary system of neutron stars powers high-energy transients, such as short gamma-ray bursts29,30,31,32,33,34,35,36,37 and kilonovae38,39,40,41,42,43,44,45,46. This unique multi-messenger detection5 showed the potential of multi-messenger astronomy impacting our knowledge of relativistic astrophysics36,37,165,166, radioactively powered transients, nucleosynthesis and heavy-element enrichment of the Universe47,48,49,50,51,52, and the physics of dense nuclear matter132,167,168,169,170,171. It also showed the importance of population studies required to disentangle the microphysics of the source and its interaction with the environment, from the source geometry and energetics. Increasing the number of joint detections will make it possible to determine the equation of state of neutron stars171, to probe the properties of different components of the mass ejected during and after the merger172,173,174, to understand if the BNS mergers are the primary channel of formation of heavy elements and the details of the nuclear physics relevant to nucleosynthesis175, and to understand the structure of the relativistic jets and the physics behind their formation176,229 will be used to further minimize shot and QRPN. The requisite non-linear optical devices (such as phase modulators) exist at 1.06 μm but are in need of significant development at longer wavelengths.

Laser power

Shot noise is the dominant limit to interferometer sensitivities at high frequencies in a simple interferometer. The choice of mirror substrate material dictates the choice of laser wavelength, which leads to constraints of the laser technologies that can be used. Lasers operating at one micron can be scaled to 500 W with the required frequency/intensity stability and mode quality230; however, development work is needed to achieve the required power and stability for lasers operating in the 1.5–2.1 μm range.

Low-frequency performance

The low-frequency observing cut-off is a critical parameter for 3G detectors. Increasing sensitivity to lower frequencies below 10–20 Hz (where the current generation of detectors operate) will enable detections of intermediate-mass black hole mergers in the range of 102–104 M⊙ and shed light on how heavier black holes form. Mirror suspension systems currently have fundamental resonances in the 1-Hz range; future detectors’ suspensions must push to lower resonant frequencies for greater isolation in the 1–10-Hz range. Suspension stages may need to be made from silicon or sapphire, which can be cooled to reduce thermal noise. Minimizing Newtonian noise necessitates finding a site with low environmental noise. An underground location (as is planned for ET) should reduce the Newtonian noise, although requires care in preserving the quiet environment through observatory design. In addition, Newtonian noise subtraction approaches231 need to be designed and tested to reach the planned factor of ten reduction to meet ET and CE performance goals.

Observatory network configuration

Multi-messenger astronomy requires accurate and relatively precise localization of GW events. The current network currently has four km-scale observatories in operation: LIGO Hanford, LIGO Livingston, Virgo and KAGRA. The addition of LIGO-India later this decade will further improve the sky localization capability18. Detailed studies of networks232,233 show that a third detector to complement ET or CE in the Southern Hemisphere — needed for detecting the majority of the events within z ~ 1.5, with error boxes less than 10 deg2 — would form a powerful array, and studies are ongoing in Australia for possible implementation.

Interferometer vacuum systems

Observatory vacuum systems are a critical infrastructure component for 3G observatories. The laser light used to probe the arm lengths must travel in an ultrahigh vacuum to avoid path-length fluctuations due to the polarizability of residual gas, and the beam tube must not introduce scattered light. As it is currently envisioned, CE will require two 40-km beam tubes, of 1.2 m diameter, at pressures less than 10−9 torr, with stringent requirements on partial pressures of molecular hydrogen, water and select hydrocarbons. As the vacuum system comprises much of the cost of a 3G observatory, ‘value engineering’ these systems is a high priority. Efforts are already underway exploring the use of low-carbon steel and nested vacuum systems234.

Civil engineering

Whether the new observatories are nominally on the surface of the Earth (such as CE) or underground (such as ET), there will be significant costs associated with the civil engineering. Site location, acquisition and preparation can present significant practical challenges, and can impact the configuration of a worldwide array.

Addressing these primary challenges (and many other challenges not discussed here) will require a sustained and globally coordinated R&D programme to be undertaken before ET and CE conceptual designs can be finalized. To have operating 3G detectors in the 2030s, facility construction should commence in this decade, requiring R&D and prototy** efforts currently underway to be ramped up significantly. Several efforts are of sufficiently large scale that industrial partnerships will be essential to succeed. Examples include the development of mirror optical coatings and mirror substrates with the requisite optical and mechanical properties. Also essential in the near term is the development of a prototype interferometer test bed for interferometry and laser development at the laboratory scale.

On a longer term, upgrading one or more of the existing LIGO facilities to a full km-scale interferometer using 3G technologies is a particularly appealing path to a full-scale 3G interferometer network in that it will both test 3G technologies almost ‘at scale’ and deliver a detector with considerably more sensitivity than the current second-generation detectors. The LIGO Voyager detector design98 is being explored as a possible upgrade to the existing LIGO observatories late in this decade. Voyager can potentially achieve a twofold sensitivity increase when compared against Advanced LIGO Plus. In addition, the Neutron star Extreme Matter Observatory (NEMO, ref.235) has been proposed in Australia as a 4-km observatory targeting neutron star GW astrophysics, aiming to have sensitivity comparable with ET and CE at frequencies above 2 kHz.

Future space-based detectors

Space-based detectors measure differential strain using an approach that is similar to that of their terrestrial counterparts. The primary difference between space-based designs such as LISA (Fig. 11 and ref.planetary ephemerides have been found to be too inaccurate for PTA experiments, but a new software package can properly model these ephemeris errors while performing the GW searches86,254.

Other issues that must be carefully considered include: long-term pulse profile evolution, the ability to accurately model changes in the electron column density along the line of sight and pulse jitter (pulse–pulse deviations from the average). Pulse jitter is pulsar-dependent and defines a minimum dwell time regardless of telescope sensitivity to achieve a given timing precision. For the celebrated bright MSP PSR J0437–4715, observations of less than an hour can never achieve residuals below 40 ns. Others, such as PSR J1909–3744, have much lower levels of jitter, nearer 10 ns. Timing arrays are starting to factor jitter limits into their observing plans so that large-aperture facilities are not ‘wasted’ on targets that do not benefit from increased SNRs.

Looking further into the future (see, for example, ref.255), the SKA and the proposed ngVLA will further enhance detection and science prospects, and China has other large-aperture radio telescopes planned, such as the 110-m **ngjiang QTT. Existing timing limits are near where many models predicted the stochastic background might be, and there is a good chance that an individual source may be separable from the background within the next decade. The major threat to PTA science is the increasingly crowded radio spectrum from satellites, aircraft and ground-based transmitters that increasingly use the once sparsely populated 300-MHz to 3-GHz band for terrestrial navigation and communications.

Conclusions

In just a few years of using instruments capable of recording the waveforms of signals, ground-based GW observatories have made seminal contributions to the fields of GR, fundamental physics and astrophysics. The multi-messenger characterization of the first observable BNS coalescence dramatically enhanced our understanding of extreme states of nuclear matter and the astrophysics of kilonovae.

The scientific potential for the field of GW science in the next few decades is considerable, afforded by the prospects of upgrades to existing observatories in this decade and the construction or launch of new observatories in the 2030s. There are clear paths to improvements in both the sensitivity of the instruments and the range of frequencies. For ground-based detectors, sensitive to astrophysics of up to ~1,000-M⊙ compact objects, the network of detectors of 3-km and 4-km scale will both improve and grow in the coming decade, and the future planned ET and CE observatories offer the possibility of a quieter environment, implementation of detectors of greater complexity and longer arms. Hence, all stellar-mass coalescing BBH systems in the Universe will be within detection reach.

The LISA space-based detector will deliver sensitivity to signals from SMBHs, with exquisite resolution of signal waveforms and completing the survey of the Universe for binaries up to some 106 M⊙. The PTAs will continue to evolve with new antenna networks, more sensitive and wider-band receivers, and discovery of additional pulsar ‘clocks’, providing unique information on the dynamics of the very largest galaxies in the Universe. Together with EM and particle detectors, these instruments will provide quantitative and qualitative new insights into physics, astrophysics, cosmology and astronomy. GW detectors have, indeed, opened a new window onto the Universe.