In a curvature-coupled propagation framework for modified gravity, gravitational-wave lensing in wave optics shows persistent infrared interactions that prevent the amplification factor from approaching unity at zero frequency, requiring an interacting Green function and partial-wave treatment.
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The Science of the Einstein Telescope
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abstract
Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.
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- abstract Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collaps
- background We comment throughout on implications for attempts to build model-agnostic waveform template banks for exotic compact objects. I. INTRODUCTION Since the first detection of gravitational waves (GWs) from a black hole (BH) binary merger [1], both the num- ber and accuracy of GW events recorded have rapidly increased [2-4]. With next-generation detectors such as the Einstein Telescope [5], Cosmic Explorer [6] and the Laser Interferometer Space Antenna (LISA) [7] on the horizon, both the frequency b
- background lease from the European Pulsar Timing Array - V. Search for continuous gravitational wave signals, Astron. Astro- phys.690, A118 (2024), arXiv:2306.16226 [astro-ph.HE]. [7] A. Abacet al.(ET), The Science of the Einstein Tele- scope, (2025), arXiv:2503.12263 [gr-qc]. [8] E. D. Hall, Cosmic Explorer: A Next-Generation Ground-Based Gravitational-Wave Observatory, Galax- ies10, 90 (2022). [9] P. Amaro-Seoaneet al.(LISA), Laser Interferometer Space Antenna, (2017), arXiv:1702.00786 [astro-ph.IM]. [10
- background binary black holes, binary neutron stars, and neutron-star-black-hole mergers [2-5]. In parallel, pulsar-timing-array observations have reported evidence for a nanohertz stochastic gravitational-wave background, opening a comple- mentary low-frequency window onto the gravitational-wave universe [6-9]. Looking ahead, the next generation of ground- and space-based detectors-including the Einstein Telescope [10], Cosmic Explorer [11], LISA [12], Tian- Qin [13], Taiji [14], and decihertz missions su
- background here provide a key ingredient for isolating the local-in-time component of the conservative two-body dynamics of binary inspirals at 5PM order. I. INTRODUCTION The advent of gravitational-wave (GW) astronomy, together with ambitious future observatories such as LISA [1], Cosmic Explorer [2] and the Einstein Tele- scope [3], has restored the relativistic two-body prob- lem in General Relativity into a central role [4]. Much of the recent progress is organized around two comple- mentary viewpoints
- background dynamics and vacuum energy in bumblebee gravity, (2026), arXiv:2601.07102 [gr-qc]. [43] B. P. Abbott et al. (LIGO Scientific, Virgo), Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett.116, 061102 (2016), arXiv:1602.03837 [gr-qc]. [44] K. G. Arun et al. (LISA), New horizons for fundamen- tal physics with LISA, Living Rev. Rel.25, 4 (2022), arXiv:2205.01597 [gr-qc]. [45] A. Abac et al. (ET), The Science of the Einstein Telescope, (2025), arXiv:2503.12263 [gr-qc].
- background scope: a comparison of different designs, JCAP07, 068, arXiv:2303.15923 [gr-qc]. [6] A. Abacet al.(ET), The Science of the Einstein Tele- scope (2025), arXiv:2503.12263 [gr-qc]. [7] D. Reitzeet al., Cosmic Explorer: The U.S. Contribu- tion to Gravitational-Wave Astronomy beyond LIGO, Bull. Am. Astron. Soc.51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]. [8] M. Evanset al., Cosmic Explorer: A Submission to the NSF MPSAC ngGW Subcommittee (2023), arXiv:2306.13745 [astro-ph.IM]. [9] M. Colpiet al.(L
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representative citing papers
Nonlocal-in-time conservative tail contributions to gravitational scattering are derived at 5PM and 10SF orders, expressed via polylogarithms up to weight three and agreeing with prior results through 6PN.
A contrastive self-supervised convolutional autoencoder detects core-collapse supernova gravitational waves with performance comparable to supervised CNNs, better generalization to unseen waveforms, and ~120 kpc sensitive distance under Einstein Telescope noise.
For infinitely differentiable effective potentials describing the post-inflation transition, the regularized power spectrum of primary gravitational waves exhibits exponential suppression at small scales.
Tensor-induced non-Gaussianity from primordial gravitational waves generates a unique scale-dependent halo bias correction that can reach order-one amplitude for rare high-redshift halos at z=7.
Bumblebee gravity perturbations decouple exactly into gravitational and vector sectors, with gravitational modes dynamically immune to Lorentz violation and odd-even parities strictly isospectral.
Axial tidal Love numbers for black holes in anisotropic fluid environments are derived analytically and numerically, with non-compact support density profiles producing logarithmic terms that obstruct standard tidal matching due to the lack of a strictly vacuum exterior.
Derives large-eccentricity asymptotics for post-Newtonian eccentric waveform Fourier modes and builds a fast endpoint-constrained analytic approximation with error under 10^{-3} valid to p=200.
GreyRing model based on greybody factors reproduces numerical relativity ringdown signals with mismatches of order 10^{-6} and enables a new post-merger consistency test of general relativity applied to GW250114.
The Squashed Pyramid Interferometer Network uses a non-coplanar configuration to directly access the chirality of cosmological gravitational waves.
A general relativistic derivation of gravitational wave response in an optically levitated cavity sensor reveals position-dependent strain sensitivity and suppressed input-mirror noise coupling.
Cordierite-based resonators with ULE mirrors reach effective CTE near zero over tens of Kelvin via mirror deflection compensating spacer expansion.
Exact non-singular black holes from the phantom DBI field evaporate to gram-mass relics, opening a new mass window for primordial black holes as dark matter.
Self-force theory is extended to compute merger and ringdown waveforms in beyond-GR black hole binaries under the extreme mass-ratio approximation, with first calculations of self-force corrections to the merger waveform.
A unified framework for the perturbed Kepler problem derives modified eccentric orbits and gravitational wave imprints from a general perturbed potential, offering a source-specific alternative to post-Newtonian expansions.
Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.
Numerical simulations of eccentric Proca-star mergers show that relative phase between the stars controls post-merger fate and can generate odd-mode gravitational waves absent from black-hole mergers.
Amortized neural posterior estimation reproduces nested sampling constraints on RMF couplings for neutron-star EOS with no bias and generates 30,000 samples in 2.5 seconds.
Numerical simulations of collapsing scalarized neutron stars show scalar radiation energy of order 10^{-3} solar masses, orders of magnitude above the tensor quadrupolar emission, potentially observable to test modified gravity.
Using simulated binary black hole mergers and neutral hydrogen maps, the radio sirens method constrains H0 to 8% precision with 3000 high-SNR events, offering a 90% improvement over standard dark siren analyses.
New simulations show that cross-correlating gravitational wave background anisotropies with galaxy distributions can enable discovery at angular scales of 4-6 degrees with next-generation observatories.
Neural network surrogate approximates precessing compact binary gravitational waveforms up to 1000x faster than the base EOB model with validated accuracy.
pyEFPEHM extends prior PN models to include higher-order quasi-circular phasing, generalized precession solutions, and eccentric corrections up to 1PN in selected multipoles for eccentric precessing binaries with matter effects.
Increasing tidal deformation around a black hole drives bound geodesics through weak chaos, plunging, unbinding, and eventual depletion of all bound motion, with semi-analytic critical amplitudes for each transition.
citing papers explorer
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Wave-optics gravitational wave lensing in modified gravity
In a curvature-coupled propagation framework for modified gravity, gravitational-wave lensing in wave optics shows persistent infrared interactions that prevent the amplification factor from approaching unity at zero frequency, requiring an interacting Green function and partial-wave treatment.
-
Nonlocal-in-time tail effects in gravitational scattering to fifth Post-Minkowskian and tenth self-force orders
Nonlocal-in-time conservative tail contributions to gravitational scattering are derived at 5PM and 10SF orders, expressed via polylogarithms up to weight three and agreeing with prior results through 6PN.
-
Contrastive self-supervised convolutional autoencoder for core-collapse supernova gravitational-wave detection
A contrastive self-supervised convolutional autoencoder detects core-collapse supernova gravitational waves with performance comparable to supervised CNNs, better generalization to unseen waveforms, and ~120 kpc sensitive distance under Einstein Telescope noise.
-
Primary gravitational waves at high frequencies II: Emergence of the exponential cut-off in the power spectrum
For infinitely differentiable effective potentials describing the post-inflation transition, the regularized power spectrum of primary gravitational waves exhibits exponential suppression at small scales.
-
Tracing Primordial Gravitational Waves via non-Gaussian Signatures of Halo Bias
Tensor-induced non-Gaussianity from primordial gravitational waves generates a unique scale-dependent halo bias correction that can reach order-one amplitude for rare high-redshift halos at z=7.
-
Gravitational-Bumblebee perturbations: Exact decoupling and isospectrality
Bumblebee gravity perturbations decouple exactly into gravitational and vector sectors, with gravitational modes dynamically immune to Lorentz violation and odd-even parities strictly isospectral.
-
Axial tidal Love numbers of black holes in matter environments
Axial tidal Love numbers for black holes in anisotropic fluid environments are derived analytically and numerically, with non-compact support density profiles producing logarithmic terms that obstruct standard tidal matching due to the lack of a strictly vacuum exterior.
-
Large-Eccentricity Asymptotics and Fast Analytic Approximation for Fourier modes of Post-Newtonian Eccentric Waveforms
Derives large-eccentricity asymptotics for post-Newtonian eccentric waveform Fourier modes and builds a fast endpoint-constrained analytic approximation with error under 10^{-3} valid to p=200.
-
Novel ringdown tests of general relativity with black hole greybody factors
GreyRing model based on greybody factors reproduces numerical relativity ringdown signals with mismatches of order 10^{-6} and enables a new post-merger consistency test of general relativity applied to GW250114.
-
Squashed Pyramid Interferometer Network (SPIN): Direct Access to Chirality of Cosmological Gravitational Waves
The Squashed Pyramid Interferometer Network uses a non-coplanar configuration to directly access the chirality of cosmological gravitational waves.
-
Gravitational wave signal and noise response of an optically levitated sensor in a Fabry-P\'erot cavity
A general relativistic derivation of gravitational wave response in an optically levitated cavity sensor reveals position-dependent strain sensitivity and suppressed input-mirror noise coupling.
-
Cordierite-based optical resonators with extremely low thermal expansion
Cordierite-based resonators with ULE mirrors reach effective CTE near zero over tens of Kelvin via mirror deflection compensating spacer expansion.
-
Exact, non-singular black holes from a phantom DBI Field as primordial dark matter
Exact non-singular black holes from the phantom DBI field evaporate to gram-mass relics, opening a new mass window for primordial black holes as dark matter.
-
Black hole mergers beyond general relativity: a self-force approach
Self-force theory is extended to compute merger and ringdown waveforms in beyond-GR black hole binaries under the extreme mass-ratio approximation, with first calculations of self-force corrections to the merger waveform.
-
Generalized Perturbed Kepler Problem: Gravitational Wave Imprints from Eccentric Compact Binaries
A unified framework for the perturbed Kepler problem derives modified eccentric orbits and gravitational wave imprints from a general perturbed potential, offering a source-specific alternative to post-Newtonian expansions.
-
Quantum production of gravitational waves after inflation
Scalar metric perturbations after inflation break conformal invariance and induce quantum production of gravitons, generating a GW spectrum that peaks near GHz frequencies for standard primordial scalar power spectra.
-
Eccentric mergers of binary Proca stars
Numerical simulations of eccentric Proca-star mergers show that relative phase between the stars controls post-merger fate and can generate odd-mode gravitational waves absent from black-hole mergers.
-
Amortized Simulation-Based Inference of Relativistic Mean-Field Couplings for Neutron-Star Equations of State
Amortized neural posterior estimation reproduces nested sampling constraints on RMF couplings for neutron-star EOS with no bias and generates 30,000 samples in 2.5 seconds.
-
Rapidly Rotating Neutron Star Collapse in Massive Scalar-Tensor Theories
Numerical simulations of collapsing scalarized neutron stars show scalar radiation energy of order 10^{-3} solar masses, orders of magnitude above the tensor quadrupolar emission, potentially observable to test modified gravity.
-
Radio sirens: inferring $H_0$ with binary black holes and neutral hydrogen in the era of the Einstein Telescope and the SKA Observatory
Using simulated binary black hole mergers and neutral hydrogen maps, the radio sirens method constrains H0 to 8% precision with 3000 high-SNR events, offering a 90% improvement over standard dark siren analyses.
-
Prospects for multi-messenger discovery of the gravitational-wave background anisotropies via cross-correlation with galaxies
New simulations show that cross-correlating gravitational wave background anisotropies with galaxy distributions can enable discovery at angular scales of 4-6 degrees with next-generation observatories.
-
Fast neural network surrogate for multimodal effective-one-body gravitational waveforms from generically precessing compact binaries
Neural network surrogate approximates precessing compact binary gravitational waveforms up to 1000x faster than the base EOB model with validated accuracy.
-
Post-Newtonian inspiral waveform model for eccentric precessing binaries with higher-order modes and matter effects
pyEFPEHM extends prior PN models to include higher-order quasi-circular phasing, generalized precession solutions, and eccentric corrections up to 1PN in selected multipoles for eccentric precessing binaries with matter effects.
-
The relativistic restricted three-body problem: geometry and motion around tidally perturbed black holes
Increasing tidal deformation around a black hole drives bound geodesics through weak chaos, plunging, unbinding, and eventual depletion of all bound motion, with semi-analytic critical amplitudes for each transition.
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Comparing next-generation detector configurations for high-redshift gravitational wave sources with neural posterior estimation
Neural posterior estimation shows a two-misaligned-L ET network yields better sky and volume localization for high-redshift massive BBHs than triangular ET, with fewer multimodalities, though luminosity distance estimates are less precise.
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Improved Identification of Strongly Lensed Gravitational Waves with Host Galaxy Locations
A two-step Bayesian reweighting scheme using Euclid galaxy locations boosts the Bayes factor for true lensed GW pairs by a factor of about 10 while lowering it for unlensed coincidences.
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Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors
Excitation factors of long-lived quasinormal modes in horizonless compact objects scale with their small imaginary frequency, suppressing early contributions and producing a hierarchy where prompt ringdown uses ordinary modes and late echoes use cavity modes.
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Inferring neutron-star Love-Q relations from gravitational waves in the hierarchical Bayesian framework
Hierarchical Bayesian inference on 20 high-SNR simulated binary neutron star events shows a linear lnΛ-lnQ relation suffices and constrains dynamical Chern-Simons gravity length scale to ≤10 km.
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Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
Extended 1PA self-force waveforms for slowly spinning primary and precessing secondary, with re-summed 1PAT1R variant showing improved accuracy against NR for q ≳ 5 and |χ1| ≲ 0.1.
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GWTC-4.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation
Statistical redshifts inferred from mass spectrum features and galaxy catalogs for 142 GW events yield H0 = 76.6 km s^{-1} Mpc^{-1} and Ξ0 = 1.2, consistent with general relativity.
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Distinguishing Neutron Star vs. Low-Mass Black Hole Binaries with Late Inspiral & Postmerger Gravitational Waves $-$ Sensitivity to Transmuted Black Holes and Non-Annihilating Dark Matter
Future high-frequency-sensitive GW detectors can distinguish binary neutron star from low-mass black hole mergers in late phases, enabling separation of merger rates and constraints on heavy non-annihilating dark matter via transmuted black holes.
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Mock Catalogs of Strongly Lensed Gravitational Waves via a Halo Model Approach with Space-borne Detectors
Mock catalogs GW-LMC-Space predict 0-131 lensed MBHB events for 4-year LISA (prob. up to 0.3%) and 0-44 for 1-year DECIGO (prob. ~0.15%), with signal overlap noted as common.
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Nucleosynthesis in the fast ejecta of a neutron star merger
Free neutrons survive r-process freeze-out in fast ejecta of neutron star mergers and their beta-decay heating produces a visible early kilonova precursor for mass fractions above ~0.05.
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Black Hole Binary Detection Landscape for the Laser Interferometer Lunar Antenna (LILA): Signal-to-Noise Calculations & Science Cases
LILA can detect IMBH binaries at redshifts 20-30, IMRIs, and provide months-to-years early warnings with high-SNR events for gravity tests.
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How do the LIGO-Virgo-KAGRA's Heavy Black Holes Form? No evidence for core-collapse Intermediate-mass black holes in GWTC-4
No evidence for core-collapse formed low-spin IMBHs in GWTC-4, with 90% upper limit on merger rate of 0.077 Gpc^{-3} yr^{-1}, low-spin BH mass truncation at 65 solar masses consistent with pair-instability gap lower edge, and high-spin IMBHs from hierarchical mergers.
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Parameter Estimation Horizon of Core-Collapse Supernovae with Current and Next-Generation Gravitational-Wave Detectors
Machine learning extracts core rotation and signal properties from CCSN gravitational waves, with next-generation detectors constraining rotation beyond 100 kpc for favorable orientations despite some uncertainties.
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Reviving Motivated Inflationary Potentials with $K$-inflation in the light of ACT
K-inflation with non-canonical kinetic term G(φ) shifts α-attractor T-models and natural inflation into the Planck-ACT-LB-BK18 allowed region while satisfying Swampland conjectures and producing testable GW spectra.
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Hawking area law in quantum gravity
Exact Hawking area law from black hole mergers restricts quantum gravity to singular Ricci-flat or specific regular black holes in Stelle and nonlocal theories, derives the standard entropy-area law, and realizes Barrow fractal black holes.
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Black Hole-Boson Star Binaries: Gravitational Wave Signals and Tidal Disruption
Numerical simulations of black hole-boson star binaries show that scalar self-interactions can suppress tidal disruption while radiative efficiency depends on the chosen potential.
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Are Black Holes Fuzzballs? Probing Horizon-Scale Structure with LISA
LISA can constrain non-axisymmetric mass quadrupole deformations at the 10^{-3} level and axisymmetric mass octupole deformations at the 10^{-2} level in EMRI signals to test fuzzball proposals.
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Confronting eikonal and post-Kerr methods with numerical evolution of scalar field perturbations in spacetimes beyond Kerr
Numerical simulations benchmark the eikonal and post-Kerr approximations for quasinormal modes in deformed Kerr spacetimes, quantifying their errors relative to expected observational precision.
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GW231123: Overlapping Gravitational Wave Signals?
GW231123 data favors an overlapping two-signal model over a single merger with Bayes factors of 100-10000, mitigating waveform-dependent discrepancies and suggesting possible gravitational lensing.
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Gravitational-wave parameter estimation to the Moon and back: massive binaries and the case of GW231123
LGWA could observe more than one third of known binary black hole events, detect ~90 mergers per year, and measure chirp mass better than third-generation detectors for massive systems.
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Primary gravitational waves at high frequencies I: Origin of suppression in the power spectrum
Adiabatic regularization combined with smoothed transitions suppresses the high-frequency oscillations in the power spectrum of primary gravitational waves about a zero mean.
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LISA as a probe of pre-big-bang physics: a nested sampling analysis
Nested sampling analysis indicates LISA could constrain H1, m, sigma_i and beta in the pre-big-bang model to relative uncertainties of about 18 percent under favorable conditions when including foregrounds.
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Dynamical Tidal Response of Non-rotating Black Holes: Connecting the MST Formalism and Worldline EFT
Renormalized dynamical tidal response functions for non-rotating black holes in GR carry inevitable ambiguities from renormalization scheme and flow initial condition, yielding scheme-dependent dynamical tidal Love numbers after MST-worldline EFT matching.
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Seeds to success: growing heavy black holes in dense star clusters
Simulations indicate stellar collisions dominate intermediate-mass black hole formation across cluster types, with potential to explain local globular cluster candidates and predict wandering IMBHs in Milky Way-like galaxies.
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Synergy between CSST and third-generation gravitational-wave detectors: Inferring cosmological parameters using cross-correlation of dark sirens and galaxies
Forecasts that cross-correlating 3G GW dark sirens with CSST photometric galaxies yields 1.04% precision on H0 and 2.04% on Omega_m while also constraining GW clustering bias.
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On the use of the Derivative Approximation for Likelihoods for Gravitational Wave Inference
DALI extends the Fisher Matrix to higher orders and approximates MCMC posteriors for GW events at 55 times lower cost, with singlet-DALI offering better accuracy and the GWDALI code providing automatic differentiation and modern waveforms.
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Impact of facility timing and coordination for next-generation gravitational-wave detectors
Simulations of ET and CE networks show delays degrade localization metrics far more than SNR, with LIGO India greatly reducing the impact for multi-messenger and stochastic searches.