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.

The Gravitational-Wave Transient Catalog (GWTC) is a collection of short-duration (transient) gravitational-wave signals identified by the LIGO–Virgo–KAGRA Collaboration in gravitational-wave data produced by the eponymous detectors. The catalog provides information about the identified candidates, such as the arrival time and amplitude of the signal and properties of the signal’s source as inferred from the observational data. GWTC is the data release of this dataset, and version 4.0 extends the catalog to include observations made during the first part of the fourth LIGO–Virgo–KAGRA observing run up until 2024 January 31. This Letter marks an introduction to a collection of articles related to this version of the catalog, GWTC-4.0. The collection of articles accompanying the catalog provides documentation of the methods used to analyze the data, summaries of the catalog of events, observational measurements drawn from the population, and detailed discussions of selected candidates.

Relations between the nuclear symmetry energy coefficient and its density derivatives are derived. The relations hold for a class of interactions with quadratic momentum dependence and a power-law density dependence. The structural connection between the different symmetry energy elements as obtained seems to be followed by almost all reasonable nuclear energy density functionals, both relativistic and nonrelativistic, suggesting a universality in the correlation structure. This, coupled with known values of some well-accepted constants related to nuclear matter, helps in constraining values of different density derivatives of the nuclear symmetry energy, shedding light on the isovector part of the nuclear interaction.

We detail the population properties of binary neutron star, neutron star–black hole binary, and binary black hole mergers using 158 events from the cumulative Gravitational-Wave Transient Catalog 4.0. The black hole primary mass distribution consists of a power-law-like continuum that steepens above 35 M _⊙ with overdensities at 10 M _⊙ and 35 M _⊙ . Binary black holes with primary masses near 10 M _⊙ are more likely to have less massive secondaries, with a mass ratio distribution peaking at q = 0.7 1 − 0.11 + 0.12 , potentially a signature of stable mass transfer during binary evolution. Black hole spins are inferred to be nonextremal, with 90% of black holes having χ < 0.6, and preferentially aligned with binary orbits, implying many merging binaries form in isolation. However, we find that a significant fraction, 0.23–0.41, of binaries have negative effective inspiral spins, suggesting many could be formed dynamically in gas-free environments. We find evidence for correlation between effective inspiral spin and mass ratio, driven either by variation in the mode of the distribution or the width. The binary black hole merger rate increases with redshift, consistent with the cosmic star formation density. While there is no evidence of the mass spectrum evolving with redshift, the distribution of effective inspiral spin is found to broaden as redshift increases out to z ≈ 1. We infer the local merger rates (at z = 0) to be 8.8–250 Gpc ⁻³ yr ⁻¹ for binary neutron stars, 9.3–86 Gpc ⁻³ yr ⁻¹ for neutron star–black hole binaries, and 13–26 Gpc ⁻³ yr ⁻¹ for binary black holes; all values reflect central 90% credible intervals.

The next generation of ground-based gravitational-wave detectors, the Einstein Telescope and Cosmic Explorer, present a unique opportunity to put constraints on dense matter, among many other groundbreaking scientific goals. In a recent study, the science case of the Einstein Telescope was further strengthened, studying in particular the performances of different detector designs. In this paper we present a more detailed study of the nuclear physics section of that work. In particular, focusing on two different detector configurations (the single-site triangular-shaped design and a design consisting of two widely separated “L-shaped” interferometers), we study the detection prospects of binary neutron star (BNS) mergers, and how they can reshape our understanding of the underlying equation of state (EOS) of dense matter. We employ several state-of-the-art EOS models and state-of-the-art synthetic BNS merger catalogs, and we make use of the Fisher information formalism to quantify statistical errors on the astrophysical parameters describing individual BNS events. To check the reliability of the Fisher information formalism method, we further perform a full parameter estimation for a few simulated events. Based on the uncertainties on the tidal deformabilities associated to these events, we outline a mechanism to extract the underlying injected EOS using a recently developed metamodeling approach within a Bayesian framework. Our results suggest that with $\gtrsim 500$ events with signal-to-noise ratio greater than 12, we will be able to pin down very precisely the underlying EOS governing the neutron star matter.

The need to reconcile our understanding of the behavior of hadronic matter across a wide range of densities, especially at the time when data from multimessenger observations and novel experimental facilities are flooding in, has provided new challenges to the nuclear models. Particularly, the density dependence of the isovector channel of the nuclear energy functionals seems hard to pin down if experiments like PREX-II (or PREX) and CREX are required to be taken on the same footing. We put to test this anomaly in a semiagnostic modeling technique by performing a full Bayesian analysis of static properties of neutron stars, together with global properties of nuclei as binding energy, charge radii and neutron skin calculated at the semiclassical level. Our results show that the interplay between bulk and surface properties, and the importance of high-order empirical parameters that effectively decouple the subsaturation and the supersaturation density regime, might partially explain the tension between the different measurements and observations. If the surface behaviors, however, are decoupled from the bulk properties, then we found a rather harmonious situation among experimental and observational data.