Dual active galactic nuclei (AGNs) are expected in hierarchical galaxy evolution models, in which low-mass galaxies merge to build more massive ones. While observational evidence for dual AGNs is growing in massive galaxies, no clear detection has yet been found in the low-mass regime. We used photometry and spectroscopy from the first Quick Data Release, combined with a collection of multi-wavelength data from the Dark Energy Spectroscopic Instrument (DESI), the LOw-Frequency ARray (LOFAR) high band antenna, and counterparts in X-ray and mid-infrared catalogues to identify dual AGNs at redshift z ≲ 1. Focusing on low-mass galaxies with stellar masses below 10^10 M_⊙, we find nine dual AGN candidates with projected separations ranging from ∼20 to 51 kpc. We also find 49 dual AGN candidates in more massive galaxies. We derive a dual AGN fraction of 0.1% for the low-mass galaxies and estimate that these systems likely trace a population of progenitor black hole pairs that may evolve into bound binaries and eventually coalesce, emitting gravitational waves in the LISA band. These results constitute the first sample of spectroscopically confirmed dual AGN candidates in low-mass galaxies and have important implications for models in which supermassive black holes grow from lower-mass black holes located in low-mass galaxies, as well as for predictions of gravitational waves from low-mass binary black holes.

Our comprehension of the history of star formation at z > 3 strongly relies on rest-frame ultraviolet observations. However, this selection systematically misses the dustiest and most massive sources, resulting in an incomplete census at earlier times. Infrared facilities such as Spitzer and the James Webb Space Telescope have shed light on a hidden population lying at z = 3 − 6 characterised by extreme red colours named HIEROs (HST-to-IRAC extremely red objects), identified by the colour criterion HE − ch2 > 2.25. Recently, Euclid Early Release Observations (EROs) have opened the possibility to further study such objects, exploiting the comparison between Euclid and ancillary Spitzer/IRAC observations. The aim of this study was to investigate the effectiveness of this synergy in characterising the population of a small test area of 232 arcmin2. We utilised catalogues in the Perseus field across the VIS and NISP bands, supplemented by data from the four Spitzer channels and several ground-based MegaCam bands (u, g, r, Hα, i, and z) already included in the ERO catalogue. We selected 121 HIEROs by applying the HE − ch2 > 2.25 colour cut, cleaned this sample of globular clusters and brown dwarfs, and then inspected by eye the multi-band cutouts of each source, ending with 42 reliable HIEROs. Photometric redshifts and other physical properties of the final sample were estimated using the spectral-energy-distribution-fitting software Bagpipes. From the zphot and M* values, we computed the galaxy stellar mass function at 3.5 < z < 5.5. When we exclude all galaxies that could host an active galactic nucleus, or whose stellar masses might be overestimated, we still find that the high-mass end of the galaxy stellar mass function is similar to previous estimates, indicating that the true value could be even higher. This investigation highlights the importance of a deeper study of this still mysterious population, in particular to assess its contribution to the cosmic star-formation rate density and its agreement with current galaxy evolution and formation models. These early results demonstrate Euclid’s capabilities to push the boundaries of our understanding of obscured star formation across a wide range of epochs.

ESA’s Euclid cosmology mission relies on the very sensitive and accurately calibrated spectroscopy channel of the Near-Infrared Spectrometer and Photometer (NISP). With three operational grisms in two wavelength intervals, NISP provides diffraction-limited slitless spectroscopy over a field of 0.57 deg2. A blue grism, BGE, covers the wavelength range 926–1366 nm at a spectral resolution (ℛ) of 440–900 for a 0.″5 diameter source with a dispersion of 1.24 nm px−1. Two red grisms, RGE, span 1206 to 1892 nm at ℛ = 550–740 and a dispersion of 1.37 nm px−1. We describe the construction of the grisms as well as the ground testing of the flight model of the NISP instrument, where these properties were established.

Context . The performance of the Euclid system is defined in terms of image quality metrics tuned to the weak gravitational lensing cosmological probe. The weak lensing measurement induces stringent requirements on the shape and stability of the VIS instrument system point spread function (PSF). The PSF is affected by error contributions from the telescope, the focal plane, and image motion, and it is controlled by a global error budget, with error allocations for each contributor. Aims . During development of the spacecraft, we verified through a structural-thermal-optical performance (STOP) analysis that the built and verified telescope with its spacecraft interface meets the in-orbit steady-state and transient image quality requirements under temperature-induced loads in all permitted spacecraft attitudes after all permitted attitude transitions. Based on data from its first year in orbit, we compared the performance we expected with the actual performance. Methods . For the purposes of the STOP analysis, we set up a detailed finite-element mathematical model and defined a standard set of test cases, both steady-state and transient, comprising combinations of worst-case boundary conditions. Iterations of the analysis were performed in conjunction with the major reviews of the spacecraft verification cycle. After launch, we applied the model in sensitivity analyses using realistic boundary conditions. Results . The STOP analysis addressed the interaction of all spacecraft components in transmitting temperature-induced loads that lead to optical train deformation. The results of the prelaunch analysis demonstrated that temperature-induced optical perturbations would be well below the allowable limits for all permitted observing conditions. We used the STOP analysis predictions to help interpret the measured performance of the spacecraft as a function of environmental variables during its first year in orbit. We discovered unpredicted disturbances (heat pulses from instrument operation propagating into the telescope), and unexpected sensitivities (e.g. a high dependence of the telescope baseplate temperature on the solar aspect angle; a nearly absent dependence on the azimuth angle after the attitude domain was redefined for stray light avoidance). In-orbit temperature variations are small (<300 mK) and so are their effects on the telescope structure (displacements <1 μm, rotations <1 μrad), but they are detected in the time histories of the image quality metrics and are a non-negligible factor in the point spread function stability budget demanded by the weak lensing science (Δ e < 2×10 −3 over 11 000 s). Taking everything into account, our analysis confirms the overall excellent performance of the telescope.

The Euclid mission of the European Space Agency seeks to understand the Universe’s expansion history and the nature of dark energy, through measurements of cosmic shear. This requires a very accurate estimate of the true redshift distribution of the galaxies, with the systematic error in the mean redshift satisfying σ⟨z⟩ < 0.002(1 + z) per tomographic bin. Achieving this accuracy relies on reference samples with spectroscopic redshifts, together with a procedure to match them to survey sources for which only photometric redshifts are available. One important source of systematic uncertainty is the mismatch in photometric properties between galaxies in the Euclid survey and the reference objects. We develop a method to degrade the photometry of objects with deep photometry to match the properties of any shallower survey in the multi-band photometric space, preserving all the correlations between the fluxes and their uncertainties. We compare our transfer method with more demanding image-based methods, such as Balrog from the Dark Energy Survey Collaboration. According to our metrics, our method outperforms Balrog. We implement our method in the redshift distribution reconstruction, based on the self-organising map approach, and test it using a realistic sample from the Euclid Flagship Mock Galaxy Simulation. We find that the key ingredient is to ensure that the reference objects are distributed in the colour space the same way as the wide-survey objects, which can be efficiently achieved with our transfer method. In our best implementation, the mean redshift biases are consistently reduced across the tomographic bins, bringing a significant fraction of them within the Euclid accuracy requirements in all tomographic bins. Equally importantly, the tests allow us to pinpoint which step in the calibration pipeline has the strongest impact on achieving the required accuracy. Our approach also reproduces the overall redshift distributions, which are crucial for applications such as angular clustering. The agreement between the reconstructed and true distributions demonstrates both the feasibility and robustness of the approach. This implementation is sufficient for Euclid Data Release 1 and provides a solid foundation for subsequent data releases.

The Euclid mission seeks to understand the Universe expansion history and the nature of dark energy, which requires a very accurate estimate of redshift distribution. Achieving this accuracy relies on reference samples with spectroscopic redshifts, together with a procedure to match them to survey sources for which only photometric redshifts are available. One important source of systematic uncertainty is the mismatch in photometric properties between galaxies in the Euclid survey and the reference objects. We develop a method to degrade the photometry of objects with deep photometry to match the properties of any shallower survey in the multi-band photometric space, preserving all the correlations between the fluxes and their uncertainties. We compare our transfer method with more demanding image-based methods, such as Balrog from the Dark Energy Survey Collaboration. According to metrics, our method outperforms Balrog. We implement it in the redshift distribution reconstruction, based on the self-organising map approach of arXiv:1509.03318, and test it using a realistic sample from the Euclid Flagship Simulation. We find that the key ingredient is to ensure that the reference objects are distributed in the colour space the same way as the wide-survey objects, which can be efficiently achieved with our transfer method. In our best implementation, the mean redshift biases are consistently reduced across the tomographic bins, bringing a significant fraction of them within the Euclid accuracy requirements in all tomographic bins. Equally importantly, the tests allow us to pinpoint which step in the calibration pipeline has the strongest impact on achieving the required accuracy. Our approach also reproduces the overall redshift distributions, which are crucial for applications such as angular clustering.

With about 1.5 billion galaxies expected to be observed, the very large number of objects in the Euclid photometric survey will allow for precise studies of galaxy clustering from a single survey, over a large range of redshifts, 0.2 < z < 2.5. In this work, we use photometric redshifts at the 68% confidence level, which represents a three-fold improvement over current constraints from the Dark Energy Survey. As expected, the constraining power in the analysis of each redshift bin is lower, with an uncertainty ranging from ±,1.23 to ±,0.289. From these results, we constrain extract the baryon acoustic oscillation signal (BAO) from the Flagship galaxy mock catalogue with a tomographic approach to constrain the evolution of the Universe and infer its cosmological parameters. We measured the two-point angular correlation function in 13 redshift bins. A template-fitting approach was applied to the measurement to extract the shift of the BAO peak through the transverse Alcock--Paczynski parameter α. A joint analysis of all redshift bins was performed to constrain α at the effective redshift z_ =0.77 with Markov chain Monte Carlo and profile likelihood techniques. We also extracted one α_i parameter per redshift bin to quantify its evolution as a function of time. From these 13 α_i, which are directly proportional to the ratio D_ /r_ , we constrain the product of the reduced Hubble constant and the sound horizon at the drag epoch, h,r_ _ eff A d and the matter density parameter Omm. From the joint analysis, we constrain D_ /r_ =10.764^ A d +0.0839 -0.0849 +0.074 _ -0.059 and h,r_ =99.35^ d +4.29 _ -4.55 , . We quantify the influence of analysis choices such as the template, scale cuts, and redshift bins, and systematic effects such as redshift-space distortions, over our constraints, both at the level of the extracted α_i parameters and at the level of cosmological inference. Mpc

The Euclid space telescope of the European Space Agency (ESA) is designed to provide sensitive and accurate measurements of weak gravitational lensing distortions over wide areas on the sky. Here, we present a weak gravitational lensing analysis of early Euclid observations obtained for the field around the massive galaxy cluster Abell 2390 as part of the Euclid Early Release Observations (ERO) programme. We conducted shape measurements for galaxies down to IE ≲ 26.5 using three independent algorithms (LensMC, KSB+, and SourceXtractor++). Incorporating multi-band photometry from Euclid and Subaru/Suprime-Cam, we estimated photometric redshifts to preferentially select background sources from tomographic redshift bins, for which we calibrated the redshift distributions using the self-organising map approach and data from the Cosmic Evolution Survey (COSMOS). We quantified the residual cluster member contamination and corrected for it in bins of photometric redshift and magnitude using their source density profiles, including corrections for source obscuration and magnification. We reconstructed the cluster mass distribution and jointly fit the tangential reduced shear profiles of the different tomographic bins with spherical Navarro-Frenk-White profile predictions to constrain the cluster mass, finding consistent results for the three shape catalogues and good agreement with earlier measurements. As an important validation test, we compared these joint constraints to mass measurements obtained individually for the different tomographic bins, finding a good level of consistency. More detailed constraints on the cluster properties are presented in a companion paper, which additionally incorporates strong lensing measurements. Our analysis provides a first demonstration of the outstanding capabilities of Euclid for tomographic weak lensing measurements.

The Euclid satellite will provide data on the clustering of galaxies and on the distortion of their measured shapes, which can be used to constrain and test the cosmological model. However, the increase in precision places strong requirements on the accuracy of the theoretical modelling for the observables and of the full analysis pipeline. In this paper, we investigate the accuracy of the calculations performed by the Cosmology Likelihood for Observables in Euclid (CLOE), a software able to handle both the modelling of observables and their fit against observational data for both the photometric and spectroscopic surveys of Euclid, by comparing the output of CLOE with external codes used as benchmark. We perform such a comparison on the quantities entering the calculations of the observables, as well as on the final outputs of these calculations. Our results highlight the high accuracy of CLOE when comparing its calculation against external codes for Euclid observables on an extended range of operative cases. In particular, all the summary statistics of interest always differ less than 0.1 σ from the chosen benchmark, and CLOE predictions are statistically compatible with simulated data obtained from benchmark codes. The same holds for the comparison of correlation function in configuration space for spectroscopic and photometric observables.

We present an example cluster follow-up study with Euclid. Our target, a z ∼ 1.74 candidate cluster nicknamed the ‘Puddle’, was initially discovered by the Massive and Distant Clusters of WISE Survey 2 as a zphot ∼ 1.65 candidate cluster. It was also detected independently as a zphot ∼ 1.5 candidate with the two cluster-finding algorithms in Euclid Quick Release 1 (Q1). A Keck MOSFIRE spectrum shows the brightest nucleus is at z = 1.74 and is dominated by an active galactic nucleus. Our analysis focused on the galaxy population and the brightest cluster galaxy (BCG), and is based on Euclid and ancillary photometry. Compared to similar fields, we measured an overdensity of 110 ± 14 galaxies with HE ≤ 22.25 in a 2′ radius around the BCG. About 18 ± 4% of the completeness-corrected galaxy population is red, which is consistent with some clusters at z > 1.5 but lower than others. Euclid imaging revealed that six or seven galaxies appear to be assembling to form the future BCG. Spectral energy distribution fitting suggests that the merging BCG has a stellar mass of 5.7 ± 0.3 × 1011 M⊙ and that it experienced a short burst of star formation ∼300 Myr ago. Its morphology and star-formation history suggest that the proto-BCG is a more evolved version of the merging core of SPT2349−56. These systems indicate that multiobject mergers might be a common BCG formation process. Assuming a similar density of mergers in the Euclid Wide Survey, we expect that Euclid will discover approximately 400 assembling BCGs by the end of its mission.

In the era of large-scale surveys such as Euclid, machine learning has become an essential tool for identifying rare yet scientifically valuable objects, such as strong gravitational lenses. However, supervised machine-learning approaches require large quantities of labelled examples to train on, and the limited number of known strong lenses has led to a reliance on simulations for training. A well-known challenge is that machine-learning models trained on one data domain often underperform when applied to a different domain: in the context of lens finding, this means that strong performance on simulated lenses does not necessarily translate into equally good performance on real observations. In the Euclid Quick Data Release 1 (Q1), covering 63 deg2, 500 strong lens candidates were discovered through a synergy of machine learning, citizen science, and expert visual inspection. These discoveries now allow us to quantify this performance gap and investigate the impact of training on real data. We find that a network trained only on simulations recovers up to 92% of simulated lenses with 100% purity, but only achieves 50% completeness with 24% purity on real Euclid data. By augmenting training data with real Euclid lenses and non-lenses, completeness improves by 25–30% in terms of the expected yield of discoverable lenses in the Euclid Data Release 1 and the full Euclid Wide Survey. Roughly 20% of this improvement comes from the inclusion of real lenses in the training data, while 5–10% comes from exposure to a more diverse set of non-lenses and false positives from Q1. We show that the most effective lens-finding strategy for real-world performance combines the diversity of simulations with the fidelity of real lenses. This hybrid approach establishes a clear methodology for maximising lens discoveries in future data releases from Euclid and will likely also be applicable to other surveys such as the Vera Rubin Observatory’s Legacy Survey of Space and Time.

The Vera C. Rubin observatory is expected to produce 10 million transient alerts per night in ugrizy filters, whilst Euclid is a visible to near-infrared space telescope engaged in a wide field survey. We present a prototype system to automatically match the transient alerts from Rubin to Euclid observations. The system produces joint light curves containing both visible and near-infrared photometry, and joint image cutouts. Using Zwicky Transient Facility alerts as a proxy for Rubin, we demonstrate the system in use in cases where Euclid did and did not detect the transient and highlight the value that can be added in each case. For transients detected by Euclid these benefits include identifying the supernovae (SNe) in observations taken prior to ground-based detection, thereby better constraining the explosion time, such as SN 2024pvw detected similar to 3d prior to ground based detections. In cases where Euclid did not detect the transient, we demonstrate the benefit of adding Euclid observations to improve host morphology measurements and associations.

The Euclid Early Release Observations (ERO) programme targeted the Perseus galaxy cluster in its central region over 0.7 deg(2). We combined the exceptional image quality and depth of the ERO-Perseus with FUV and NUV observations from GALEX and AstroSat/UVIT, as well as ugrizH alpha data from MegaCam at the CFHT, to deliver FUV-to-NIR magnitudes of the 87 brightest galaxies within the Perseus cluster. We reconstructed the star formation history (SFH) of 59 early-type galaxies (ETGs) within the sample, through the spectral energy distribution (SED) fitting code CIGALE and state-of-the-art stellar population (SP) models to reproduce the galactic UV emission from hot, old, low-mass stars (i.e. the UV upturn). In addition, for the six most massive ETGs in Perseus [stellar masses log(10)(M-*/M-circle dot)>= 10.3], we analysed their spatially resolved SP and SFH through a radial SED fitting. In agreement with our previous work on Virgo ETGs, we found that (i) the majority of the analysed galaxies needs the presence of a UV upturn component to explain their FUV emission, with average temperatures < T-UV >similar or equal to 33 800 K; (ii) the ETGs of Perseus have grown their stellar masses quickly, with star formation timescales of tau less than or similar to 1500 Myr. We found that all ETGs in the sample have formed more than about 30% of their stellar masses at z similar or equal to 5, up to extreme fractions of similar or equal to 100%. At z similar or equal to 5, the stellar masses of the most massive nearby ETGs, which have present-day stellar masses of log(10)(M-*/M-circle dot)greater than or similar to 10.8, are then found to be comparable to those of the red quiescent galaxies observed by JWST at similar redshifts (z > 4.6). This study can be extended to ETGs in the 14 000 deg(2) extragalactic sky that will soon be observed by Euclid, in combination with those from other major upcoming surveys (e.g. Rubin/LSST), and UV observations, to ultimately assess whether the massive ETGs that we observe today represent the progeny of the massive high-z JWST red quiescent galaxies.

Dual active galactic nuclei (AGNs) are expected in hierarchical galaxy evolution models, in which low-mass galaxies merge to build more massive ones. While observational evidence for dual AGNs is growing in massive galaxies, no clear detection has yet been found in the low-mass regime. We used photometry and spectroscopy from the first Euclid Quick Data Release, combined with a collection of multi-wavelength data from the Dark Energy Spectroscopic Instrument (DESI), the LOw-Frequency ARray (LOFAR) high band antenna, and counterparts in X-ray and mid-infrared catalogues to identify dual AGNs at redshift z ≲ 1. Focusing on low-mass galaxies with stellar masses below 1010 M⊙, we find nine dual AGN candidates with projected separations ranging from ∼20 to 51 kpc. We also find 49 dual AGN candidates in more massive galaxies. We derive a dual AGN fraction of 0.1% for the low-mass galaxies and estimate that these systems likely trace a population of progenitor black hole pairs that may evolve into bound binaries and eventually coalesce, emitting gravitational waves in the LISA band. These results constitute the first sample of spectroscopically confirmed dual AGN candidates in low-mass galaxies and have important implications for models in which supermassive black holes grow from lower-mass black holes located in low-mass galaxies, as well as for predictions of gravitational waves from low-mass binary black holes.

Weak lensing surveys require accurate correction for the point spread function (PSF) when measuring galaxy shapes. For a diffraction-limited PSF, as arises in space-based missions, this correction depends on each galaxy SED. In the Euclid mission, galaxy SED reconstruction, a tasks of the photometric-redshift processing function (PHZ PF), relies on broad- and medium-band ancillary photometry. The limited wavelength sampling of the Euclid VIS passband and signal-to-noise ratio may affect the reconstruction accuracy and translate into biases in the weak lensing measurements. In this study, we present the methodology, which is employed in the Euclid PHZ PF, for reconstructing galaxy SEDs at 55 wavelengths, sampling the VIS passband every 10 nm, and we assess whether it fulfils the accuracy requirements imposed on the Euclid PSF model. We employ both physics- and data-driven methods, focusing on a new approach of template-based flux correction and Gaussian processes, and we introduce an SED metric whose bias propagates into PSF quadrupole moment errors. Our findings demonstrate that Gaussian processes and template fitting meet the requirements only in specific, but complementary, redshift intervals. We therefore propose a hybrid approach, which leverages both methods. This solution proves to be effective in meeting the Euclid accuracy requirements for most of the redshift range of the survey. Finally, we investigate the impact on the SED reconstruction of a new set of 16 evenly-spaced medium-band filters for the Subaru telescope, providing quasi-spectroscopic coverage of the VIS passband. This study shows promising results, ensuring accurate SED reconstruction and meeting the mission PSF requirements. This work thus provides not only the methodological foundation of galaxy SED reconstruction in the Euclid PHZ PF, but also a roadmap for future improvements using a new medium-band survey.

We model intrinsic alignments (IA) in Euclid's Flagship simulation to investigate its impact on Euclid's weak lensing signal. Our IA implementation in the Flagship simulation takes into account photometric properties of galaxies as well as their dark matter host halos. We compare simulations against theory predictions, determining the parameters of two of the most widely used IA models: the Non Linear Alignment (NLA) and the Tidal Alignment and Tidal Torquing (TATT) models. We measure the amplitude of the simulated IA signal as a function of galaxy magnitude and colour in the redshift range 0.1<z<2.1. We find that both NLA and TATT can accurately describe the IA signal in the simulation down to scales of 6-7 h^-1Mpc. We measure alignment amplitudes for red galaxies comparable to those of the observations, with samples not used in the calibration procedure. For blue galaxies, our constraints are consistent with zero alignments in our first redshift bin 0.1 < z < 0.3, but we detect a non-negligible signal at higher redshift, which is, however, consistent with the upper limits set by observational constraints. Additionally, several hydrodynamical simulations predict alignment for spiral galaxies, in agreement with our findings. Finally, the evolution of alignment with redshift is realistic and comparable to that determined in the observations. However, we find that the commonly adopted redshift power-law for IA fails to reproduce the simulation alignments above z=1.1. A significantly better agreement is obtained when a luminosity dependence is included, capturing the intrinsic luminosity evolution with redshift in magnitude-limited surveys. We conclude that the Flagship IA simulation is a useful tool for translating current IA constraints into predictions for IA contamination of Euclid-like samples.

The well-known bimodality between star-forming discs and quiescent spheroids requires the existence of two main processes: galaxy quenching, causing the strong reduction of star formation, and morphological transformation, causing the transition from disc-dominated structures to bulge-dominated ones . In this paper, we aim to understand the link between these two processes and their relation with the stellar mass of galaxies and their local environment. Taking advantage of the first data released by the Euclid Collaboration, covering more than 60, ^2 with space-based imaging and photometry, we analyse a mass-complete sample of nearly one million galaxies in the range 0.2510^ deg 9.5 , M_⊙, using a combination of photometric and spectroscopic redshifts. We divide the sample into four sub-populations of galaxies, based on their star-formation activity (star-forming and quiescent) and morphology (disc-dominated and bulge-dominated). We then analyse the physical properties of these populations and their relative abundances in the stellar mass versus local density plane. Together with confirming the passivity-density relation and the morphology-density relation, we find that quiescent discy galaxies are more abundant in the low-mass regime of high-density environment where log_ 10 (1+δ)>1.3. At the same time, star-forming bulge-dominated galaxies are more common in field regions with log_ 10 (1+δ)<0.8, preferentially at high masses. Building on these results and interpreting them through comparison with simulations , we propose a scenario where the evolution of galaxies in the field significantly differs from that in higher-density environments. The morphological transformation in the majority of field galaxies takes place before the onset of quenching and is mainly driven by secular processes taking place within the main sequence, leading to the formation of star-forming bulge-dominated galaxies as intermediate-stage galaxies. Conversely, quenching of star formation precedes morphological transformation for most galaxies in higher-density environments. This causes the formation of quiescent disc-dominated galaxies before their transition into bulge-dominated ones.

The matter distribution around galaxy clusters is distributed over several filaments, reflecting their positions as nodes in the large-scale cosmic web. The number of filaments connected to a cluster, namely its connectivity, is expected to affect the physical properties of clusters. Using the first Euclid galaxy catalogue from the Euclid Quick Release 1 (Q1), we investigate the connectivity of galaxy clusters and how it correlates with their physical and galaxy member properties. Around 220 clusters located within the three fields of Q1 (covering ∼ 63 deg^2), are analysed in the redshift range 0.2 < z < 0.7. Due to the photometric redshift uncertainty, we reconstruct the cosmic web skeleton, and measure cluster connectivity, in 2-D projected slices with a thickness of 170 comoving h^-1.Mpc and centred on each cluster redshift, by using two different filament finder algorithms on the most massive galaxies (M_* > 10^10.3 M_⊙). In agreement with previous measurements, we recover the mass-connectivity relation independently of the filament detection algorithm, showing that the most massive clusters are, on average, connected to a larger number of cosmic filaments, consistent with hierarchical structure formation models. Furthermore, we explore possible correlations between connectivities and two cluster properties: the fraction of early-type galaxies and the Sérsic index of galaxy members. Our result suggests that the clusters populated by early-type galaxies exhibit higher connectivity compared to clusters dominated by late-type galaxies. These preliminary investigations highlight our ability to quantify the impact of the cosmic web connectivity on cluster properties with Euclid.

We present and investigate the properties of a sample of radio-selected, Euclid-dark galaxies, identified from LOFAR HBA observations at 144 MHz within the Euclid Deep Field-North (EDF-N). Starting from radio sources lacking optical counterparts in previous surveys, but detected with Spitzer/IRAC, we identified 166 galaxies with no emission at a more than 3σ level in Euclid Quick Release 1 (Q1) images, and no matches in the Euclid Q1 catalogue. To minimise contamination from nearby sources, we selected a sub-sample of 88 isolated galaxies. By exploiting multi-band images and catalogues available for the EDF-N, we inferred the physical properties of our sample via SED fitting. The resulting redshift distribution spans 0.4 ≤ z_ph≤ 5.0. We used recent sub-arcsecond imaging from the International LOFAR Telescope to constrain the nature of the compact radio emission through brightness temperature estimates. By combining this information with the radio excess relative to the infrared/radio correlation (IRRC), we searched for possible active galactic nuclei (AGN) activity. Approximately 40

As the statistical precision of cosmological measurements increases, the accuracy of the theoretical description of these measurements must correspondingly increase to infer the underlying cosmology governing the Universe. To this end, we created the Cosmology Likelihood for Observables in Euclid (CLOE), which is a novel cosmological parameter inference pipeline developed within the Euclid Consortium to translate measurements and covariances into cosmological parameter constraints. In this first in a series of five papers, we describe the theoretical recipe of this code for the Euclid primary probes. These probes are composed of the photometric 3times2pt observables of cosmic shear, galaxy-galaxy lensing, and galaxy clustering, along with spectroscopic galaxy clustering. We provide this description in both Fourier and configuration space for standard and extended summary statistics, including the wide range of systematic uncertainties that affect these statistics. This includes systematic uncertainties such as intrinsic galaxy alignments, baryonic feedback, photometric and spectroscopic redshift uncertainties, shear calibration uncertainties, sample impurities, photometric and spectroscopic galaxy biases, as well as magnification bias. The theoretical descriptions can further accommodate both Gaussian and non-Gaussian likelihoods, as well as extended cosmologies with non-zero curvature, massive neutrinos, evolving dark energy, and simple forms of modified gravity. These theoretical descriptions that underpin CLOE will form a crucial component in revealing the true nature of the Universe with next-generation cosmological surveys such as Euclid.