Welcome and general info about the workshop

• Jacopo Fumagalli (ICCUB - Universitat de Barcelona)
• Domènec Espriu (ICC - University of Barcelona)

LISA mission status and Spanish contribution

• Carlos Sopuerta (ICE-CSIC)

Spectral and dark siren cosmological analyses with LISA (Collaborative Project)

• Danny Laghi

Ongoing Collaborative project

Rapid testing of cosmological SGWB models against Global Fit residuals (Collaborative Project)

• Ameek Malhotra (Swansea University)

In this talk, we will give an update about this Cosmology WG project. This project aims to implement a methodology to test theoretical models of the cosmological contributions to the SGWB against residuals potentially found by a Global Fit run. It assumes the release of the posterior for the parameters of a free-form SGWB contribution in the shape of splines (or other interpolation schemes such as GP's). Utilising that output as a posterior predictive, we explore the possibility of inferring constraints for theoretical models of the SGWB. We will probe the limitation of this approach close to the low-signal regime, and try to derive recommendations for optimal free form reconstructions.

Gravitational Wave Strong Lensing with LISA (Collaborative Project)

• Jose Maria Ezquiaga (Niels Bohr Institute)

All signals in the Universe are at least weakly lensed, and a fraction of them will be strongly lensed. The probability of strong lensing only becomes larger at higher redshift and, therefore, LISA sources such as massive black hole binaries and extreme mass ratio inspiral are unique sources to probe strong lensing due to their cosmological distances and large signal-to-noise ratios. If strong lenses of LISA sources are identified, they can be used as precision probes of the source properties and its population, testing General Relativity and measuring cosmological parameters, enabling unique cosmological and astrophysical measurements. This project explores the rates and detectability of lensed LISA sources.

Synergy between LISA and ET (Collaborative Project)

• Gabriele Perna (KBFI)
• Antonio Junior Iovino (New York University Abu Dhabi)

The advent of third generation interferometers marks a new era for Gravitational Wave (GW) searches and will enable to shed light on both early- and late-Universe dynamics. In this context, synergies between different Gravitational Wave detectors are crucial for a better detection and characterization of a GW Background, either of cosmological or astrophysical origin. Different cosmological sources, in fact, predict a broad spectrum which could be detectable in different frequency bands. We present the first collaborative project between the LISA and the ET collaborations, which aims to explore the advantages of a synergic search between the two detectors.

Reinterpreting GW Signals from PTs in Particle Physics Model Parameter Space (Collaborative Project)

• Eric Madge (IFT-UAM/CSIC)

Once LISA provides data, the resulting constraints on, or detection of, a stochastic gravitational wave background will be analyzed in the context of various sources, particularly cosmological phase transitions. This analysis will not only cover the general characteristics of these phase transitions but also explore the underlying particle physics models that generate them. While the LISA collaboration can directly interpret the general phase transition signals, the detailed interpretation in terms of specific particle physics models — given the wide range of possible models — will require extensive input from the broader scientific community. This project aims to develop a computational tool that streamlines the reinterpretation of gravitational wave (GW) signals from cosmological phase transitions in terms of parameters of underlying particle physics models. The software will take GW signal parameters as reconstructed from simulated data — expressed either in terms of geometric parameters (characteristic frequencies, slopes, and amplitude) or thermodynamic parameters (transition strength, bubble size, temperature, and wall velocity) — and map them into the parameter space of specific particle physics models. Users will input a parameter scan, mapping model parameters (such as couplings and masses) to the corresponding GW signal parameters. The tool will then generate parameter fits, including 68% and 95% confidence level contours, within the model’s parameter space, based on provided datasets (e.g., simulated injected signals, Monte Carlo chains, or likelihood fits). This approach builds on the framework outlined in Section 6 of arXiv:2403.03723, with improvements to automate and enhance the process. In addition, a database of benchmark models and associated GW signals will be established. This will leverage existing parameter scans (such as those from the Phase Transition Parameter Estimation Project, arXiv:2403.03723) and incorporate new models and scans as needed.

Primordial black holes and their gravitational wave signatures (30+10)

• Juan Garcia-Bellido (Universidad Autonoma de Madrid)

Gravitational Wave Lensing Across the Mass Spectrum (30+10)

• Luka Vujeva (Niels Bohr Institute)

Gravitational lensing is an invaluable probe of the nature of dark matter and the structures it forms. Lensed gravitational waves in particular allow for unparalleled sensitivity to small-scale structures within lenses due to the precise time resolution combined with continuous monitoring of the entire sky. In this talk, I will explore the effects that the presence of both large and small scale dark matter structures have on lensed gravitational waves. Additionally, I will show how we can both infer the presence of substructure through observed lensed signals, and constrain the nature of dark matter through their detection. I will conclude by highlight exciting prospects for gravitational wave lensing in the strong field regime of gravity.

The kinematic dipole: why LISA should care (30+10)

• Giulia Cusin (IAP, Paris and University of Geneva)

Towards a DDPC Plan for the SGWB: Dreams vs. Hyper‑Realism (30+10)

• Germano Nardini (University of Stavanger)

The reconstruction of a cosmological stochastic gravitational-wave background (SGWB), or the derivation of its upper bounds, represents one of the key challenges for LISA. Achieving this goal requires a solid understanding of the instrumental noise, careful control of the systematics in the reconstruction of the transient sources, and reliable theoretical knowledge of both cosmological and astrophysical signals. Given these complexities, officially committing to a precise measurement and separation of the SGWB components is very risky but, on the other hand, a potential breakthrough in fundamental physics. This talk will try to outline the main perspectives surrounding this challenge and stimulate constructive feedback to help shape a realistic agenda for the LISA SGWB analysis.

Cosmological Gravitational-Wave Backgrounds in the Mojito Heavy Dataset: Generation and Analysis (30+10)

• Henri Inchauspe (KU Leuven)

The Distributed Data Processing Centre (DDPC) is developing the data analysis methods and pipelines required to fully exploit the unique observational capabilities of LISA, opening access to the millihertz band and enabling precision gravitational-wave astronomy. This may provide a pathway to probing physics beyond the last scattering surface. However, the associated data analysis challenges are substantial. To address them, the DDPC is producing a suite of common datasets of increasing complexity, designed to reflect the richness of signals expected in LISA data streams. The Mojito Heavy dataset will include three cosmological stochastic background components (provided as configurable options), spanning representative spectral morphologies: (1) a broken power-law spectrum characteristic of first-order phase transitions, (2) a double-peaked spectrum arising from scalar-induced gravitational waves, and (3) an approximately flat in-band spectrum representative of cosmic string signals. In addition, the dataset incorporates an extragalactic astrophysical foreground from compact binaries (double white dwarfs). All components are generated as isotropic in the CMB rest frame and propagated through the full LISA response, including realistic spacecraft orbits, second-generation time-delay interferometry (TDI), and representative instrumental noise. In this talk, I will present the current status of the dataset generation, planned for release in October 2026, as well as strategies for its exploitation beyond the DDPC. In particular, I will discuss approaches to cosmological signal extraction that leverage distinctive features of the signal, including Doppler-induced anisotropies, as part of a newly proposed collaborative project within the LISA Consortium Working Group.

Cosmic strings beyond minimally-coupled models (Collaborative project)

• Jeremy Wachter (Wentworth Institute of Technology)

We report on progress made on the CosWG2025-01 project, "Cosmic strings beyond minimally-coupled models". We consider the gravitational-wave background produced by strings with interactions beyond their coupling to gravity, examining several well-motivated extensions: metastable strings, superstrings, global strings, and strings moving in extra dimensions. We discuss LISA's ability to constrain the parameter space of these models based on simulations of signal recovery by SGWBinner. Finally, we comment on connections to beyond-standard-model physics and what theories could be probed by measurements of these string signals.

Simulation-based inference and gradient-based methods for gravitational-wave cosmology (30+10)

• Konstantin Leyde (CCA/Flatiron)

Gravitational-wave lensing (30+10)

• Otto Hannuksela (The Chinese University of Hong Kong (CUHK))

Einstein's relativity postulates that, similarly to light, gravitational waves can be gravitationally lensed by massive intervening objects such as galaxies, dark-matter subhalos, and compact lenses. Such gravitational lensing encodes potentially detectable signatures in the gravitational waves LISA can detect. On the one hand, the direct detection of such signatures would promise a unique avenue for science case studies. On the other hand, neglecting gravitational-wave weak lensing could lead to biased cosmological studies. Here, I review some basic results of gravitational-wave lensing relevant to LISA.

Simulation based inference for gravitational-wave background data analysis (30+10)

• Mauro Pieroni (IEM-CSIC)

Biases in SGWB Component Separation at LISA: The Impact of Inter-Template Dependencies

• Marco Finetti (University of Aveiro)

Operating in the millihertz band, LISA will probe a rich superposition of GW signals. Astrophysical population models predict a sufficient number of signals in the LISA band to blend together and form an irresolvable Galactic foreground noise. In addition, a stochastic gravitational wave background (SGWB) of cosmological origin could add an unknown component to the measured noise. A central challenge is then to separate these unknown contributions from the Galactic foreground. Current analyses build parametric templates for each population independently. I will show that, in the presence of multiple unresolved components, these templates are not independent, leading to inconsistencies when interpreting the combined signal. Using a representative SGWB model, I quantify the impact of this effect on parameter estimation. Neglecting inter-template correlations can lead to significan biases, and, for several benchmark cases, those biases exceed the statistical reconstruction uncertainties. These findings expose a key limitation of existing template-based strategies and indicate that unbiased component separation will likely require additional information, such as constraints from resolved sources obtained through global-fit analyses.

Impact of correlated noise on the reconstruction of the stochastic gravitational-wave background

• Giulia Capurri (University of Pisa)

The stochastic gravitational-wave background (SGWB) is a key science target for next-generation detectors. In this talk, I will present a Bayesian study of the impact of correlated noise on SGWB reconstruction in the triangular Einstein Telescope configuration. Using simulated data, I will show that neglecting detector correlations can significantly bias the inferred SGWB parameters, while a joint inference of signal and noise yields an unbiased recovery of both. This study provides a useful example of how such correlations can affect the SGWB inference and it is linked to the LISA data analysis where similar effects are present. More broadly, it highlights the importance of performing SGWB analyses with increasingly realistic noise models and of continuing to develop robust frameworks in which signal and instrumental noise are inferred jointly.

Constraining non-Gaussianity and chirality in Scalar-Induced Gravitational Waves with next-generation ground-based interferometers

• Ilaria Caporali (Università di Pisa - INFN Pisa)

Future gravitational-wave detectors can probe primordial non-Gaussianity and parity violation through the stochastic gravitational-wave background. In this talk, I will present a framework that includes both parity-even and parity-odd higher-order correlators. Using simulated data for next-generation detectors, like Einstein Telescope and Cosmic Explorer, I will demonstrate that these effects can be constrained even in the presence of an astrophysical foreground. The parity-odd component, in particular, leads to a circularly polarized signal, providing a direct probe of chirality in the early Universe. Finally, I will discuss how this framework can be extended to space-based detectors such as LISA, enabling a synergic detection across complementary frequency bands.

Uncertainty budgets for bubble wall velocities in cosmological phase transitions

• Philipp Schicho (University of Geneva)

First-order cosmological phase transitions could have been central to early-universe phenomena such as baryogenesis and gravitational waves (GW). Predicting such GW signatures requires not only reliable equilibrium thermodynamics but also an accurate determination of the terminal velocity of the nucleated bubbles during the transition. In this talk, I present progress towards quantifying the theoretical uncertainties of bubble wall velocities. Using the WallGo package [1] applied to extensions of the Standard Model, I will identify several order-one sources of uncertainty, including missing out-of-equilibrium species in the collision terms, treatments of thermal masses, inputs from thermal equilibrium such as the nucleation temperature, and ansatz choices for bubble profiles. By mapping out this uncertainty budget, I will highlight the most critical directions for improving the reliability of wall velocity, and thus GW predictions [2]. [1] A. Ekstedt, O. Gould, J. Hirvonen, B. Laurent, L. Niemi, P. Schicho, and J. van de Vis, How fast does the WallGo? A package for computing wall velocities in first-order phase transitions, JHEP 04, 101 (2025),[2411.04970]. [2] J. van de Vis, P. Schicho, L. Niemi, B. Laurent, J. Hirvonen, O. Gould, WallGo investigates: Theoretical uncertainties in the bubble wall velocity, [2510.27691].

Weak lensing of standard sirens

• Ville Vaskonen (KBFI)

Weak gravitational lensing induces scatter in measurements of the luminosity distance-redshift relation. I show that incorporating weak lensing in standard siren analyses enables new probes of cosmic structure. As an illustration, I present a forecast for measuring the variance of matter perturbations, alongside the Hubble constant and matter abundance, using simulated bright sirens representative of ET and LISA observations.

Testing gravitational wave polarizations with LISA

• Alberto Mangiagli (AEI)
• Macarena Lagos (Universidad Andres Bello)

We quantify the ability of LISA to test the presence of non-tensorial polarizations as well as modifications to the tensor ones in gravitational waves emitted from massive black hole binaries. We employ the Parametrized Post-Einsteinian (PPE) formalism to model deviations from General Relativity for tensor, vector, and scalar polarizations. Our PPE parametrization is inspired by post-Newtonian waveforms from four modified gravity theories: Horndeski, Einstein-aether, Rosen's bimetric, and Lightman-Lee. We consistently implement these modifications across the inspiral, merger, and ringdown phases, ensuring proper waveform alignment and tapering. Subsequently, we perform Fisher forecasts to derive expected constraints on deviations from General Relativity and map these constraints to the parameter spaces of the four gravity theories. This work demonstrates LISA's potential to probe gravity in the strong-field regime via gravitational wave polarizations. https://docs.google.com/presentation/d/1PZfxtCBGAg2ewBgF7Xvf0UxwswceTPu39ztTY4U1k5M/edit?usp=sharing

Towards a realistic forecast on the ability of LISA to measure cosmic strings (30+10)

• Daniel Figueroa (Valencia U., IFIC)

GUEST: Gravitational Universe Exploration with Satellite Tracking (30+10)

• Diego Blas (ICREA/IFAE)

I intrude GUEST, a new proposal to ESA F3 call to find GWs in the band 1e-6 to 1e-4 and that can be in the sky contemporarily to LISA.

Gravitational waves from cosmological phase transitions: sound waves and turbulence (30+10)

• Alberto Roper Pol (University of Geneva)

Understanding stochastic gravitational wave backgrounds by exploring the parameter space of first-order phase transitions with the Sound Shell Model

• Mika Mäki (University of Helsinki)

Cosmological first-order phase transitions can generate stochastic gravitational wave backgrounds observable by LISA, offering a probe of physics beyond the Standard Model. Extracting phase transition parameters from LISA observations requires comparing observations to theoretical predictions across a high-dimensional parameter space. However, running a full lattice simulation for each parameter point is prohibitively expensive. We address this challenge using the [Sound Shell Model](https://arxiv.org/abs/1909.10040), a computationally efficient framework that reproduces the results of lattice simulations for intermediate-strength transitions. We have implemented the Sound Shell Model in the Python-based simulation library [PTtools](https://github.com/CFT-HY/pttools), enabling systematic large-scale exploration of the parameter space. Our implementation incorporates key physical effects, including [variations in the sound speed](https://arxiv.org/abs/2511.20436), [thermal suppression of bubble nucleation](https://arxiv.org/abs/2205.04097), and [the finite lifetime of the acoustic source](https://arxiv.org/abs/2409.01426). In addition, we extend the web-based tool [PTPlot](https://www.ptplot.org/ptplot/) to support double broken power law (DBPL) fits and Sound Shell Model spectra, providing more accurate alternatives to the standard broken power law (BPL) approximations. These developments provide a fast and flexible framework for modeling stochastic gravitational wave signals from phase transitions, enabling likelihood-based parameter inference with LISA.

Reviving PBHs: primordial black holes from supercooled phase transitions revisited

• Piotr Toczek (University of Warsaw)

Black holes in the asteroid-mass range, $10^{15}$ - $10^{20}$ kg, provide a compelling candidate for dark matter. This window remains largely unconstrained observationally, while the low masses provide an interesting challenge in explaining their possible origin. In this talk, I will discuss a particular formation scenario of such objects, where curvature perturbations responsible for gravitational collapse into black holes are generated by a cosmological first-order phase transition. If the transition is strongly supercooled and slow compared to the Hubble expansion, fluctuations in the bubble nucleation history in different patches of the Universe can produce a large spectrum of curvature perturbations. I will present a covariant formalism that can be adopted to compute the evolution of energy-density fluctuations within a fixed comoving volume. Within this formalism, I will highlight the crucial role of energy flux carried by expanding bubble walls in amplifying curvature perturbations to the level required for black hole formation. Finally, I will identify the transitions for which the population of produced black holes can fully explain the abundance of dark matter observed today.

Probing Primordial Black Hole abundance and reheating with Scalar-Induced Gravitational Waves in the LISA band

• Gabriele Perna (KBFI)

Scalar-induced Gravitational Waves (SIGWs) represent a powerful way to probe the early-Universe. Their production is strongly affected by the evolution of the Universe as well as by the presence of primordial non-Gaussianity. In this talk I will discuss the imprints of different equation of state $w$ and speed of sound $c_s^2$ on the SIGW signal as well as the capability of LISA to constrain these different parameters accounting also for the presence of primordial non-Gaussianity. Additionally, in the specific case of a radiation dominated Universe, by analysing the interplay between Primordial Black Holes (PBHs) and SIGWs, I will show that uncertainties due to non-Gaussianity can induce substantial uncertainties in the PBH abundance, limiting LISA's capacity to fully probe the asteroid-mass PBH DM window.

Gravitational Wave Background from Cosmic Strings in Extra Dimensions

• Jun'ya Kume (University of Helsinki)

The gravitational wave (GW) signal from cosmic strings is usually modeled in the Nambu–Goto (NG) framework, where bursts from cusps and kinks determine the spectral shape of the resulting stochastic background. In higher-dimensional settings, however, string motion in the internal space alters this picture in an essential way: exact cusps are suppressed and the beaming properties of the bursts are modified. In this talk, I will discuss a phenomenological modeling of these effects and their consequences for the stochastic GW background. I will show how extra dimensions induce characteristic changes in the effective burst power and spectral tilt, while the impact of modified network evolution appears comparatively mild in the baseline treatment. I will also briefly comment on the observational consequences, including the possibility that such extra-dimensional cosmic-string spectra provide a significantly improved description of current PTA observations compared with the standard NG case.

Sky localization of LISA massive black hole binaries and the role of waveform systematics (30+10)

• Sylvain Marsat (L2IT)

Young Star Clusters: potential factories of LISA sources?

• Sara Rastello (Universitat de Barcelona)

Dense young star clusters (YSCs) are ideal environments for close encounters between stars and stellar-mass black holes, giving rise to micro-tidal disruption events (micro-TDEs) transient phenomena with potential multi-messenger signatures in both the electromagnetic and gravitational wave domains. We present results from a suite of 3600 direct N-body simulations of YSCs, performed with a customised version of the PeTar code incorporating new micro-TDE prescriptions, covering a wide range of cluster masses, densities, and metallicities. We identify three main dynamical channels: single encounters, binary-mediated interactions, and higher-order multiples. The latter dominates, accounting for ~90% of all events. The gravitational wave signal from micro-TDEs peaks in the deci-Hertz band, making them promising targets for future detectors such as LGWA and DECIGO. Combined with their expected electromagnetic signatures detectable by LSST, micro-TDEs emerge as multi-messenger probes of the dormant stellar-mass black hole population in dense stellar environments.

Resonant Excitation of Neutron Star Modes in NS-NS/NS-BH Coalescing Binaries

• Roque Márquez Rodríguez (ICCUB)

Neutron stars (NSs) experience internal oscillatory modes with characteristic frequencies that depend on their equation of state (EOS) and structure. Such modes can be resonantly excited during binary NS-BH/NS-NS inspirals, provided that the frequency of the tidal driving force exerted by the companion reaches the modes’ sufficiently before coalescence. These tidal resonances result in orbital energy being transferred to the modes, effectively reducing coalescing times and imprinting phase excesses on GW NS-NS or NS-BH inspirals [1, 2, 3]. In my talk at the LISA CosWG Meeting 2026, I can describe how accurate computations of NS modes impact multimessenger NS-NS/NS-BH observations physics of extremely dense matter (see, e.g., [4, 5]). As a first-year PhD student involved in the LISA CosWG 2026 local organizing committee, I will be happy to describe the work on GWs that is currently being carried out at the hosting institution, the Institut de Ciències del Cosmos de la Universitat de Barcelona (ICCUB), so as to help paving the way for the detection of NS resonances in future events observed by next-generation GW detectors. Our research involves computing NS modes based on EOS-informed models (using, e.g., pseudospectral collocation methods; see, e.g., [6]), calculating orbit-mode energy transfers (see Figure 1) that lead to reduced NS-NS/NS-BH coalescing times and estimating the detectability of resonance imprints in GW waveforms (see Figure 2).

Polarisation Singularities of Gravitational Waves

• Claire Rigouzzo (King's College London)

Departure from idealised plane waves gives rise to intricate geometric structures in wave fields. One such structure is the polarisation singularity, which emerges when multiple monochromatic waves interfere (such as would be the case for stochastic backgrounds), producing loci of purely circular or linear polarisation. In this work, we extend the theory of polarisation singularities to gravitational waves and higher spin fields. Building on the electromagnetic description, we formulate the gravitational analogue of polarisation singularities and show that they are generic features of gravitational waves. Their dimension, however, depends on the spin of the field. We illustrate these results with simulations of plane-wave interference and analyse the resulting singularity densities. Finally, we comment on observational effects for LISA, in particular for the gravitational wave background emitted by galactic binaries.

Discovering Cold Dark Matter with LISA via stochastic diffraction (30+10)

• Juan Urrutia (KBFI)

Stochastic Gravitational Wave Background Inference in the Global Fit using the Wavelet Domain

• Robert Rosati (NASA - Marshall / University of Alabama in Huntsville)

LISA's data will have several non-stationary stochastic components: several contributions to the instrumental noise directly depend on the arm lengths of the constellation, while others will be only quasi-stationary with slow drifts over time. Additionally, anisotropic SGWBs will show an induced non-stationarity as LISA orbits the sun. This effect will be particularly strong for the galactic foreground, but may also be present in boosted isotropic cosmological SGWBs. All of these effects combine to create a challenging non-stationary environment for an SGWB search. In the Fourier domain, this non-stationarity will induce correlations between neighboring frequencies, as well as overestimate the variance of the data in time periods with lower-than-average noise. The Wilson-Debauchies-Meyer (WDM) wavelet domain is a complete basis time-frequency representation of the data, and allows for uncorrelated basis elements in quasi-stationary data as well as tracking of the variance over time. It also has several other technical advantages over other time-frequency representations. In this talk, I will present a WDM-based SGWB pipeline developed as a global fit module for both GLASS and Erebor. It shows improved inference for cosmological signals in the presence of non-stationary noise components, and improves inference on discrete signals as well, since it is a better whitening filter for arm-varying LISA data.

Assessing PBH formation in the LISA band through CMB constraints

• Sasha Allegrini (KBFI, Tallinn and Tallinn U. Tech.)

The formation of primordial black holes (PBHs) is intrinsically connected to the generation of scalar-induced gravitational waves (SIGWs). LISA will probe gravitational waves in the mHz band, corresponding to PBHs in the asteroid-mass range, providing a powerful avenue to constrain their role as dark matter candidates. In this talk, we focus on scenarios featuring a transient ultra slow-roll (USR) phase during inflation, which can trigger PBH formation, assessing the compatibility of such models with CMB constraints and standard cosmological evolution. In particular, we evaluate their viability to generate signals in the LISA-sensitive range in light of the latest results from ACT and the Planck Collaboration, by performing an MCMC-assisted exploration of the parameter space. This work is based on Refs.~[ArXiv:2510.18791, ArXiv:2412.14049].

Concluding remarks