Complex survey selection effects, such as those present in Euclid's slitless spectroscopy, are challenging to model. In Euclid Collaboration: Granett, de la Torre, Moresco et al. (in prep), we develop simulators to apply the systematic effects to mock galaxy catalogues, such that the impact can be propagated to the cosmological inference. 

In Euclid Collaboration: Monaco, Elkhashab, Granett et al. (2025) we study the impact of angular effects on the cosmological constraints.

In the figure, we show a simulated survey area for the Euclid mission (obtained by the code developed in Euclid Collaboration: Granett, de la Torre, Moresco et al. in prep). The color indicates the density of target galaxies, which is modulated by instrumental noise, and astrophysical foregrounds including zodiacal emission.

Catastrophic errors in spectroscopic redshift measurements can introduce interlopers that severely impact the analysis and bias cosmological parameter inference. It is crucial to accurately quantify and control these systematics to ensure robust cosmological constraints from current and future spectroscopic surveys. In Euclid Collaboration: Le Brun, Bethermin, Moresco et al. (2025), we presented the code developed for the Euclid mission to perform spectroscopic measurements, which has been tested to deliver highly accurate redshift measurements when applying an optimized quality selection, with negligible bias and percent-level precision. We demonstrated that this selection can allow us to achieve a high redshift success rate in the key cosmological redshift range, enabling the construction of large and robust samples for cosmological analyses.

In the figure from Le Brun, Bethermin, Moresco et al. (2025) is shown the comparison between the redshifts measured on the same sources from Euclid data (y axis) and from a ground-based survey (DESI, x axis). Along the diagonal are found the correctly measured redshifts, while other diagonal lines represent redshift interlopers, characterized in this work.

We developed and validated a modeling approach that explicitly incorporates the contribution of redshift interlopers into the galaxy clustering likelihood. In Euclid Collaboration: Risso et al. (2025), using realistic Euclid simulations, we quantified how the effects of different interloper populations propagate through the two-point correlation function into cosmological parameter estimation, with particular focus on redshift-space distortions and baryon acoustic oscillations. A central outcome of this work is the demonstration that the impact of redshift interlopers can be successfully mitigated, for the survey area corresponding to the first Euclid Data Release (DR1), using a simple model that accounts only for the overall purity of the spectroscopic sample. However, we showed that the same modeling assumptions may not be sufficient for the full survey at the end of the mission, when the observed volume will be six times larger than that of DR1.

In Principi, Veropalumbo, Moresco et al. (2026, in prep), we extended this analysis to the 3PCF, assessing for the first time the impact of interlopers in the measurement of cosmological parameters with the 3PCF. We derived and tested new estimators to quantify the cross-correlation terms, and implemented mitigation strategies that allow us to retrieve unbiased parameters also in the presence of interlopers within an error smaller than 0.3 sigma.

In the figure from Risso et al. (2025), the cosmological parameter derived from an unbiased redshift sample is shown in grey, and the impact of redshift interlopers, when not correctly modeled, is shown in red. The green data show how it is possible to properly recover the correct parameters when the mitigation strategy is adopted.

To fully exploit the statistical power of next-generation galaxy surveys, it is fundamental to develop fast and robust algorithms capable of measuring higher-order correlation functions on extremely large datasets. In Euclid Collaboration: Veropalumbo, Moresco et al. (2026), we presented the code developed within the Euclid Science Ground Segment to measure the galaxy 3PCF, implementing and testing different estimators that achieve the required accuracy while remaining computationally feasible for the full survey. Extensive validation tests demonstrate the robustness and precision of the implementation, while performance analyses confirm the scalability of the code to Euclid data volume.

In Euclid Collaboration: Guidi, Veropalumbo, Moresco et al. (2025), we have further developed a novel emulator that, for the first time, enables a full-shape cosmological analysis by compressing the information from the combined two-point and three-point correlation functions (2PCF + 3PCF) directly into targeted cosmological parameters. This approach exploits the complementary information encoded in higher-order statistics, allowing a significant gain in constraining power beyond standard two-point analyses. In the reference paper, we validated the method using Flagship simulations that realistically reproduce Euclid galaxy clustering in real space, demonstrating that the inclusion of the 3PCF leads to a substantial tightening of cosmological constraints. The methodology has subsequently been extended to redshift space with a dedicated modelling code (Melcorr), and applied to observational data to extract cosmological constraints from the joint 2PCF + 3PCF analysis of BOSS DR12 galaxies (Guidi, Moresco et al., in prep)

After delivering the first cosmological measurements from a joint 2PCF+3PCF analysis on both Euclid simulated data and BOSS observations, in Labate, Guidi, Moresco et al. (2025) we further explored the potential of three-point statistics to constrain cosmological parameters beyond the standard model. In particular, we investigated how the 3PCF can be used to probe the imprint of massive neutrinos on large-scale structure. Using N-body simulations with varying neutrino masses, we demonstrated that neutrino free-streaming produces distinctive configuration-dependent signatures in the 3PCF, especially for elongated and squeezed triangle shapes, and that these signatures differ markedly from those induced by changes in σ8. This enables the 3PCF to be a powerful tool to break the Mν–σ8 degeneracy and opens the way to competitive neutrino-mass constraints from ongoing spectroscopic surveys such as Euclid and DESI.

In the figure (from Labate, Guidi, Moresco et al. 2025) are shown, as an illustrative example, 3PCF in different configurations (the various plots) presenting measurements obtained from simulations with different neutrino masses, compared to a fiducial ΛCDM (different colors). The lower plots show the detectabilities of different neutrino masses in the 3PCF at different scales, where the yellow shaded area shows the position of the BAO peak.

Ages as cosmological probes

A new and powerful frontier in observational cosmology is emerging through the use of time itself as a cosmological probe, in the form of cosmic clocks and cosmic chronometers (Moresco 2024, Moresco 2026). By measuring the ages of the oldest stellar populations, globular clusters, and galaxy clusters across cosmic time, these approaches provide a direct and independent determination of the expansion history of the Universe. Recent advances, from age-dating of lensed globular clusters with JWST (Tomasetti, Moresco et al. 2025a) to Galactic archaeology with Gaia (Tomasetti, Chiappini, Nepal, Moresco et al. 2025) and the development of cluster-based cosmic chronometers (Tomasetti, Moresco et al. 2025b), demonstrate that precise cosmic-age measurements are now achievable out to significant redshifts. Coupled with large-scale structure analyses, these time-based probes offer a complementary and highly synergistic route to tighten cosmological constraints and test the consistency of the standard cosmological model. Altogether, this opens a genuinely new observational window on cosmic expansion, enabling cross-checks of standard probes and offering a promising avenue to address current tensions in cosmology.

Gravitational waves and standard sirens

Gravitational waves from compact binary mergers provide an independent and self-calibrating probe of the cosmic expansion through the standard siren method. Fully exploiting this opportunity requires substantial methodological advances to cope with the computational demands of Bayesian inference, the incompleteness of galaxy catalogues used for statistical host identification, and astrophysical uncertainties in source population modelling. Recent developments, including GPU-accelerated inference pipelines (Tagliazucchi, Moresco et al. 2025), Bayesian frameworks accounting for galaxy-catalog incompleteness (Borghi, Moresco et al. 2025), and data-driven semiparametric modelling of gravitational-wave source populations (Tagliazucchi, Moresco et al. 2026), have significantly improved the robustness and precision of standard siren cosmology. These advances are particularly important in view of forthcoming deep spectroscopic surveys, as they enable a natural and powerful synergy between large-scale structure analyses and future gravitational-wave observations, ultimately leading to joint constraints on the expansion history of the Universe.