The growing number of gravitational-wave detections from binary black holes enables increasingly precise measurements of their population properties. The observed population is most likely drawn from multiple formation channels. Population-synthesis simulations allow detailed modelling of each of these channels, and comparing population-synthesis models with the observations allows us to constrain the uncertain physics of binary black hole formation and evolution. However, the most detailed population-synthesis codes are computationally expensive. We demonstrate the use of normalising flows to emulate five different population synthesis models, reducing the computational expense, and allowing interpolation between the populations predicted for different simulation inputs. With the trained normalising flows, we measure the branching ratios of different formation channels and details of binary stellar evolution, using the current catalogue of gravitational-wave observations.

The recently discovered gravitational wave event GW231123 was interpreted as the merger of two black holes with a total mass of 190-265 M circle dot, making it the heaviest such merger detected to date. While much of the postdiscovery literature has focused on its astrophysical origins, primary analyses have exhibited considerable discrepancies in the measurement of source properties between waveform models, which cannot reliably be reproduced by simulations. Such discrepancies may arise when an unaccounted overlapping signal is present in the data, or from phenomena that produce similar effects, such as gravitational lensing or overlapping noise artifacts. In this work, we analyze GW231123 using a flexible model that allows for two overlapping signals, and find that it is favored over the isolated signal model with Bayes factors of similar to 102-104, depending on the waveform model. These values lie within the top few percent of the background distribution. Similar effects are not observed in GW190521, another high-mass event. Under the overlapping signals model, discrepancies in the measurement of source properties between waveform models are largely mitigated. We also find that neglecting an additional signal in overlapping-signal data can lead to discrepancies in the estimated source properties resembling those reported in GW231123. Although the overlapping signal model provides a higher Bayesian evidence, the astrophysical prior probability of two short signals overlapping is low. However, we find that the two recovered sources show similar properties. This, taken with the higher evidence of the two signal model, suggests that gravitational lensing may provide an alternative explanation.

As gravitational-wave catalogs grow, they will become increasingly computationally expensive to analyze in their entirety, especially when inferring astrophysical source populations with high-dimensional, flexible models. Bayesian statistics offers a natural remedy, letting us update our knowledge of physical models as new data arrive, without re-analyzing existing data. However, doing so requires the posterior probability density of model parameters for previous observations, which is typically intractable. Here, we use variational neural posterior estimation to rapidly update the inferred population of binary black holes as data are observed in gravitational-wave detectors. We apply this approach to real and simulated catalogs analyzed with both low- and high-dimensional population models, testing the reliability of three update cadences: with new catalogs of sources, month by month during an observing run, and as each new signal arrives. We investigate the success and failure modes of neural sequential updates, finding that the robustness of updating is sensitive to the information contained in each update and that updating is most effective when performed with larger segments of data. We outline one additional scientific application enabled by Bayesian updating: identification of events that are individually informative about the population. Neural Bayesian updates to astrophysical population models also provide efficient likelihood representations for joint analyses with other data, e.g., standard-siren cosmology, and similar methods can be used to perform Bayesian stochastic background searches.

Artificial intelligence (AI) is transforming scientific research, with deep learning methods playing a central role in data analysis, simulations, and signal detection across particle, nuclear, and astroparticle physics. Within the JENA communities-ECFA, NuPECC, and APPEC-and as part of the EuCAIF initiative, AI integration is advancing steadily. However, broader adoption remains constrained by challenges such as limited computational resources, a lack of expertise, and difficulties in transitioning from research and development (R D) to production. This white paper provides a strategic roadmap, informed by a community survey, to address these barriers. It outlines critical infrastructure requirements, prioritizes training initiatives, and proposes funding strategies to scale AI capabilities across fundamental physics over the next five years.

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.

Gravitational waves from extreme mass-ratio inspirals (EMRIs) will enable subpercent measurements of massive black hole parameters and provide access to the demographics of compact objects in galactic nuclei. During the LISA mission, multiple EMRIs are expected to be detected, allowing statistical studies of massive black hole populations and their formation pathways. We perform hierarchical Bayesian inference on simulated EMRI catalogs to assess how well LISA could constrain the astrophysical population using parameterized population models. We test our inference framework on a variety of populations, including heterogeneous and homogeneous mixtures of parameterized subpopulations, and scenarios in which the assumed model is deliberately misspecified. Our results show that population parameters governing distributions with sharp features can be tightly constrained. Mixed populations can be disentangled with as few as similar to 20 detections, and even with model misspecification, the inference retains sensitivity to key population features. These results demonstrate the capabilities and limitations of EMRI population inference, providing guidance for constructing realistic astrophysical population models for LISA analysis.

Gravitational waves from extreme mass-ratio inspirals (EMRIs), the inspirals of stellar-mass compact objects into massive black holes, are predicted to be observed by the Laser Interferometer Space Antenna (LISA). A sufficiently large number of EMRI observations will provide unique insights into the massive black hole population. We have developed a hierarchical Bayesian inference framework capable of constraining the parameters of the EMRI population, accounting for selection biases. We leverage the capacity of a feed-forward neural network as an emulator, enabling detectability calculations of ∼10^5 EMRIs in a fraction of a second, speeding up the likelihood evaluation by ≳6 orders of magnitude. We validate our framework on a phenomenological EMRI population model. This framework enables studies of how well we can constrain EMRI population parameters, such as the slope of both the massive and stellar-mass black hole mass spectra and the branching fractions of different formation channels, allowing further investigation into the evolution of massive black holes.

Gravitational waves (GWs) from binary neutron stars (BNSs) offer a valuable understanding of the nature of compact objects and hadronic matter, and the science potential will be greatly enhanced by the third-generation (3G) GW detectors, which are expected to detect BNS signals with order-of-magnitude improvements in duration, detection rates, and signal strength. However, the resulting computational demands for analyzing such prolonged signals pose a critical challenge that existing Bayesian methods cannot feasibly address in the 3G era. To bridge this critical gap, we demonstrate a machine learning-based workflow capable of producing source parameter estimation and constraints on equations of state (EOSs) for hours-long BNS signals in seconds with minimal hardware costs. We employ efficient compression of the GW data and EOS using neural networks, based on which we build normalizing flows for inference that can deliver results in seconds. The optimized computational cost of BNS signal analysis with our framework shows that machine learning has the potential to be an indispensable tool for future catalog-level BNS analyses, paving the way for large-scale investigations of BNS-related physics across the 3G observational landscape.

Smooth window functions are often applied to strain data when inferring the parameters describing the astrophysical sources of gravitational-wave transients. Within the LIGO-Virgo-KAGRA collaboration, it is conventional to include a term to account for power loss due to this window in the likelihood function. We show that the inclusion of this factor leads to biased inference. The simplest solution to this, omitting the factor, leads to unbiased posteriors and Bayes factor estimates provided the window does not suppress the signal for signal-to-noise ratios (SNRs) less than or similar to O(100), but unreliable estimates of the absolute likelihood. Instead, we propose a multi-stage method that yields consistent estimates for the absolute likelihood in addition to unbiased posterior distributions and Bayes factors for SNRs less than or similar to O(1000). Additionally, we demonstrate that the commonly held wisdom that using rectangular windows necessarily leads to biased inference is incorrect.

Progress in gravitational-wave (GW) astronomy depends upon having sensitive detectors with good data quality. Since the end of the Laser Interferometer Gravitational-Wave Observatory-Virgo-KAGRA third Observing run in March 2020, detector-characterization efforts have lead to increased sensitivity of the detectors, swifter validation of GW candidates and improved tools used for data-quality products. In this article, we discuss these efforts in detail and their impact on our ability to detect and study GWs. These include the multiple instrumental investigations that led to reduction in transient noise, along with the work to improve software tools used to examine the detectors data-quality. We end with a brief discussion on the role and requirements of detector characterization as the sensitivity of our detectors further improves in the future Observing runs.

We present the results of a search for gravitational-wave transients associated with core-collapse supernova SN 2023ixf, which was observed in the galaxy Messier 101 via optical emission on 2023 May 19, during the LIGO–Virgo–KAGRA 15th Engineering Run. We define a five-day on-source window during which an accompanying gravitational-wave signal may have occurred. No gravitational waves have been identified in data when at least two gravitational-wave observatories were operating, which covered ∼14% of this five-day window. We report the search detection efficiency for various possible gravitational-wave emission models. Considering the distance to M101 (6.7 Mpc), we derive constraints on the gravitational-wave emission mechanism of core-collapse supernovae across a broad frequency spectrum, ranging from 50 Hz to 2 kHz, where we assume the gravitational-wave emission occurred when coincident data are available in the on-source window. Considering an ellipsoid model for a rotating proto-neutron star, our search is sensitive to gravitational-wave energy 1 × 10 −4 M ⊙ c 2 and luminosity 2.6 × 10 −4 M ⊙ c 2 s −1 for a source emitting at 82 Hz. These constraints are around an order of magnitude more stringent than those obtained so far with gravitational-wave data. The constraint on the ellipticity of the proto-neutron star that is formed is as low as 1.08, at frequencies above 1200 Hz, surpassing past results.

We present results from a search for X-ray/gamma-ray counterparts of gravitational-wave (GW) candidates from the third observing run (O3) of the LIGO-Virgo-KAGRA network using the Swift Burst Alert Telescope (Swift-BAT). The search includes 636 GW candidates received with low latency, 86 of which have been confirmed by the offline analysis and included in the third cumulative Gravitational-Wave Transient Catalogs (GWTC-3). Targeted searches were carried out on the entire GW sample using the maximum-likelihood Non-imaging Transient Reconstruction and Temporal Search pipeline on the BAT data made available via the GUANO infrastructure. We do not detect any significant electromagnetic emission that is temporally and spatially coincident with any of the GW candidates. We report flux upper limits in the 15-350 keV band as a function of sky position for all the catalog candidates. For GW candidates where the Swift-BAT false alarm rate is less than 10(-3) Hz, we compute the GW-BAT joint false alarm rate. Finally, the derived Swift-BAT upper limits are used to infer constraints on the putative electromagnetic emission associated with binary black hole mergers.

Bayesian inference with stochastic sampling has been widely used to obtain the properties of gravitational wave (GW) sources. Although computationally intensive, its cost remains manageable for current second-generation GW detectors because of the relatively low event rate and signal-to-noise ratio (SNR). The third-generation (3G) GW detectors are expected to detect hundreds of thousands of compact binary coalescence (CBC) events every year with substantially higher SNR and longer signal duration, presenting significant computational challenges. In this study, we systematically evaluate the computational costs of CBC source parameter estimation (PE) in the 3G era by modeling the PE time cost as a function of SNR and signal duration. We examine the standard PE method alongside acceleration methods including relative binning, multibanding, and reduced order quadrature. We predict that PE for a one-month-observation catalog with 3G detectors could require at least billions of CPU core hours with the standard PE method, whereas acceleration techniques can reduce this demand to less than millions of core hours, which is as high as the cost of analyzing GW events in the past 10 years. These findings highlight the necessity for more efficient PE methods to enable cost-effective and environmentally sustainable data analysis for 3G detectors. In addition, we assess the accuracy of accelerated PE methods, emphasizing the need for careful treatment in high-SNR scenarios.

Binary population synthesis simulations allow detailed modelling of gravitational-wave sources from a variety of formation channels. These population models can be compared to the observed catalogue of merging binaries to infer the uncertain astrophysical input parameters describing binary formation and evolution, as well as the relative rates between various formation pathways. However, it is computationally infeasible to run population synthesis simulations for all variations of uncertain input physics. We demonstrate the use of normalizing flows to emulate population synthesis results and interpolate between astrophysical input parameters. Using current gravitational-wave observations of binary black holes, we use our trained normalizing flows to infer branching ratios between multiple formation channels, and simultaneously infer common-envelope efficiency and natal spins across a continuous parameter range. Given our set of formation channel models, we infer the natal spin to be 0.04(-0.01)(+0.04), and the common-envelope efficiency to be >3.7 at 90% credibility, with the majority of underlying mergers coming from the common-envelope channel. Our framework allows us to measure population synthesis inputs where we do not have simulations, and better constrain the astrophysics underlying current gravitational-wave populations.

Gravitational wave data are often contaminated by non-Gaussian noise transients, glitches, which can bias the inference of astrophysical signal parameters. Traditional approaches either subtract glitches in a pre-processing step, or a glitch model can be included from an agnostic wavelet basis (e.g. BayesWave). In this work, we introduce a machine-learning-based approach to build a parameterised model of glitches. We train a normalising flow on known glitches from the Gravity Spy catalogue, constructing an informative prior on the glitch model. By incorporating this model into the Bayesian inference analysis with Bilby, we estimate glitch and signal parameters simultaneously. We demonstrate the performance of our method through bias reduction, glitch identification and Bayesian model selection on real glitches. Our results show that this approach effectively removes glitches from the data, significantly improving source parameter estimation and reducing bias.

On May 24, 2023, the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), joined by the Advanced Virgo and KAGRA detectors, began the fourth observing run for a two-year-long dedicated search for gravitational waves. The LIGO Hanford and Livingston detectors have achieved an unprecedented sensitivity to gravitational waves, with an angle-averaged median range to binary neutron star mergers of 152 and 160 Mpc, and duty cycles of 65.0% and 71.2%, respectively, with a coincident duty cycle of 52.6%. The maximum range achieved by the LIGO Hanford detector is 165 Mpc and the LIGO Livingston detector 177 Mpc, both achieved during the second part of the fourth observing run. For the fourth run, the quantum-limited sensitivity of the detectors was increased significantly due to the higher intracavity power from laser system upgrades and replacement of core optics, and from the addition of a 300 m filter cavity to provide the squeezed light with a frequency-dependent squeezing angle, part of the Athorn upgrade program. Altogether, the Athorn upgrades led to reduced detector-wide losses for the squeezed vacuum states of light which, alongside the filter cavity, enabled broadband quantum noise reduction of up to 5.2 dB at the Hanford observatory and 6.1 dB at the Livingston observatory. Improvements to sensors and actuators as well as significant controls commissioning increased low frequency sensitivity. This paper details these instrumental upgrades, analyzes the noise sources that limit detector sensitivity, and describes the commissioning challenges of the fourth observing run.

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) searches for gamma-ray/X-ray counterparts to gravitational wave (GW) candidate events identified during the third observing run of the Advanced LIGO and Advanced Virgo detectors. Using Fermi-GBM on-board triggers and sub-threshold gamma-ray burst (GRB) candidates found in the Fermi-GBM ground analyses, the Targeted Search and the Untargeted Search, we investigate whether there are any coincident GRBs associated with the GWs. We also search the Swift-BAT rate data around the GW times to determine whether a GRB counterpart is present. No counterparts are found. Using both the Fermi-GBM Targeted Search and the Swift-BAT search, we calculate flux upper limits and present joint upper limits on the gamma-ray luminosity of each GW. Given these limits, we constrain theoretical models for the emission of gamma-rays from binary black hole mergers.

The discovery of gravitational waves, first observed in September 2015 following the merger of a binary black hole system, has already revolutionised our understanding of the Universe. This was further enhanced in August 2017, when the coalescence of a binary neutron star system was observed both with gravitational waves and a variety of electromagnetic counterparts; this joint observation marked the beginning of gravitational multimessenger astronomy. The Einstein Telescope, a proposed next-generation ground-based gravitational-wave observatory, will dramatically increase the sensitivity to sources: the number of observations of gravitational waves is expected to increase from roughly 100 per year to roughly 100'000 per year, and signals may be visible for hours at a time, given the low frequency cutoff of the planned instrument. This increase in the number of observed events, and the duration with which they are observed, is hugely beneficial to the scientific goals of the community but poses a number of significant computing challenges. Moreover, the currently used computing algorithms do not scale to this new environment, both in terms of the amount of resources required and the speed with which each signal must be characterised. This contribution will discuss the Einstein Telescope's computing challenges, and the activities that are underway to prepare for them. Available computing resources and technologies will greatly evolve in the years ahead, and those working to develop the Einstein Telescope data analysis algorithms will need to take this into account. It will also be important to factor into the initial development of the experiment's computing model the availability of huge parallel HPC systems and ubiquitous Cloud computing; the design of the model will also, for the first time, include the environmental impact as one of the optimisation metrics.

The Heisenberg uncertainty principle dictates that the position and momentum of an object cannot be simultaneously measured with arbitrary precision, giving rise to an apparent limitation known as the standard quantum limit (SQL). Gravitational-wave detectors use photons to continuously measure the positions of freely falling mirrors and so are affected by the SQL. We investigated the performance of the Laser Interferometer Gravitational-Wave Observatory (LIGO) after the experimental realization of frequency-dependent squeezing designed to surpass the SQL. For the LIGO Livingston detector, we found that the upgrade reduces quantum noise below the SQL by a maximum of three decibels between 35 and 75 hertz while achieving a broadband sensitivity improvement, increasing the overall detector sensitivity during astrophysical observations.

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass $M>70$ $M_\odot$) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities $0 < e \leq 0.3$ at $0.33$ Gpc$^{-3}$ yr$^{-1}$ at 90\% confidence level.