Michael L. Brown

The Euclid mission has been designed to provide, as one of its main deliverables, information on the nature of the gravitational interaction, which determines the expansion of the Universe and the formation of structures. Thus, Euclid has the potential to test deviations from general relativity that will allow us to shed light on long-lasting problems in the standard cosmological Λ cold dark matter model, ΛCDM. Euclid will mainly do this by using two complementary probes: weak gravitational lensing and galaxy clustering. In this paper we review pre-launch Euclid analyses for dark energy and modified gravity. These include forecast constraints with future Euclid data on cosmological parameters for different cosmological models, such as a time-varying dark energy component, phenomenological modifications of the perturbation sector and specific modified gravity models, with further extensions that include neutrino physics and the coupling to the electromagnetic sector through the fine-structure constant. We review the study of the impact of non-linear clustering methods on beyond-ΛCDM constraints with Euclid . This is of fundamental importance to efficiently predict the large-scale clustering of matter and dark matter haloes, given that we will have access to a wealth of information on scales beyond the linear regime. We inspect the extension of theoretical predictions for observable quantities in alternative cosmologies to ΛCDM at fully non-linear scales by means of N -body simulations. We discuss the impact of relativistic corrections in extended cosmological models. Overall, this review highlights the significant potential of the Euclid mission to tightly constrain parameters of dark energy and modified gravity models, or perhaps to detect possible signatures of a ΛCDM failure.

The Euclid spacecraft, located at the second Lagrangian point of the Sun-Earth system, hosts the Near-Infrared Spectrometer and Photometer (NISP) instrument. NISP is equipped with a mosaic of 16 HgCdTe-based detectors (Teledyne’s H2RG) to acquire near-infrared photometric and spectroscopic data. To meet the spacecraft’s constraints on computational resources and telemetry bandwidth, the near-infrared signal is processed on board via a dedicated hardware-software architecture designed to fulfil Euclid ’s stringent data quality requirements. A custom application software, running on the two NISP data-processing units, implements the NISP signal estimator: an ad hoc algorithm that delivers accurate flux measurements and simultaneously estimates the quality of signal estimation through the quality factor (QF) parameter. This paper further investigates the properties of the NISP signal estimator by evaluating its performance during the early flight operations of the NISP instrument. First, we revisit the assumptions on which the inference of the near-infrared signal is based and investigate the origin of the main systematics of the signal estimator through Monte Carlo simulations. Then, we explain how we tested the flight performance of the NISP signal estimator. Results indicate a systematic bias lower than 0.01 e ⁻ s ⁻¹ for 99% of the NISP pixel array, which is well within the noise budget of the estimated signal. We also derived an analytical expression for the variance of the NISP signal estimator, demonstrating its validity, particularly when the covariance matrix is not pre-computed. Finally, we provide a robust statistical framework to interpret the QF parameter, analyse its dependence on the signal estimator bias, and show its sensitivity to cosmic-ray hits on NISP detectors. Our findings corroborate previous results on the NISP signal estimator and suggest a leading-order correction based on the agreement between flight data and simulations.

Stage-IV galaxy surveys will provide the opportunity to test cosmological models and the underlying theory of gravity with unparal-leled precision. In this context, it is crucial for the Euclid mission to leverage its spectroscopic and photometric probes to systematically investigate and incorporate non-standard cosmological models, including modified gravity, alternative dark energy scenarios, massive neutrinos, and primordial non-Gaussianity. For this, we produce and release publicly simulated galaxy catalogues from a broad suite of non-standard cosmological simulations, which we processed through a model-independent analytical pipeline, making use of ROCKSTAR for halo identification, and a modified version of the SciPic library for the galaxy-halo connection using the halo occupation distribution framework. One of the goals of this paper is also to test the validity of the template-fitting method for galaxy clustering analyses, even in cases where the template significantly differ from data. For this purpose, we investigate the multipoles of the two-point correlation function in redshift space and VDG _∞ , a highly performant, state-of-the-art model for galaxy clustering. Across a wide range of models, the linear growth rate multiplied by the matter density within spheres of radius of 12 Mpc, fσ ₁₂ , exhibits a notable robustness to the choice of cosmological template. Compared to previous works, our study extends this result to numerous scenarios with markedly distinct gravitational or dark energy dynamics. We find that the most of the scatter in cosmological parameter inference already appears when using the cosmological model of the simulations as templates. Using a ‘wrong’ template can also introduce an additional scatter, although with smaller amplitude. Often, we find deviations much larger than error bars, meaning that the Gaussian approximation for the covariance might need to be further studied. Looking ahead, future cosmological investigations must broaden their scope to include a diverse array of non-standard theoretical frameworks extending beyond ΛCDM and rudimentary dynamic dark energy models.

We present the first end-to-end validation of the Euclid baryon acoustic oscillation (BAO) analysis pipeline, encompassing density-field reconstruction, two-point correlation function measurement, and cosmological parameter inference. Using eight Euclid -like mock catalogues extracted from each of the four snapshots of the Flagship 1 (FS1) simulation, which is designed to replicate the statistical properties of the first Euclid data release (DR1), we assessed the performance of the two standard BAO reconstruction methods based on the Zeldovich approximation, R EC S YM and R EC I SO , in four redshift snapshots (0.9 ≤ z ≤ 1.8). The pipeline introduces several methodological advances: an emulator-based model evaluator ( Bora.jl ) combined with a Hamiltonian Monte Carlo sampler ( NUTS ), achieving a speed-up of more than 500 times relative to standard Monte Carlo Markov chains, and a semi-analytical covariance estimator ( BeXiCov+WinCov ) that enables robust error estimates with only eight mock realisations and remains stable under variations in the fiducial cosmology. Together, these components ensure computational efficiency while significantly reducing the risk of underestimating the parameter uncertainties. The two reconstruction schemes yield unbiased BAO measurements for all redshifts and user-defined choices, including the smoothing scale and fiducial cosmology. In each snapshot, reconstruction enhances the figure of merit for {Ω _m , H ₀ r _s } by a factor of ∼3, which is equivalent to tripling the effective survey volume. When we combined the four redshift bins, the improvement remained substantial, with BAO-only constraints reaching ∼10% precision on Ω _m and ∼3% on H ₀ r _s . The results from R EC S YM and R EC I SO are consistent within the uncertainties, but we recommend R EC S YM during testing because its sensitivity to covariance variations is lower. These findings establish the accuracy, robustness, and scalability of the Euclid BAO pipeline for DR1 and provide a solid foundation for future cosmological analyses.

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), covering approximately 10 deg ² . Starting from 1051 radio sources lacking optical counterparts down to a 5σ depth of 23.9 in the y band in previous surveys (but detected with Spitzer /IRAC), we identified 166 galaxies with no emission at a depth of more than 3σ from Euclid Quick Release 1 (Q1) images, reaching a 5σ depth of 23.9 in the H _E band, 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 made use of recent sub-arcsecond imaging from the International LOFAR Telescope over an area of 2.5 deg × 2.5 deg to constrain the nature of the compact radio emission in our targets 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 nucleus (AGN) activity in our sample. Approximately 30% of our sources show a radio excess relative to star formation. This fraction increases to 40% when including AGNs identified via their brightness temperature. The Euclid -dark sources detected in the far-infrared (FIR) are consistent with a population of heavily obscured (⟨ A _V ^ISM ⟩ = 5.0) massive (⟨log ₁₀ ( M _⋆ / M _⊙ )⟩ = 11.6) star forming galaxies (SFGs) with high star formation rates (⟨log ₁₀ (SFR/ M _⊙ yr ⁻¹ )⟩ = 3.3). Their location above the star-forming main sequence is consistent with the high-mass and high-SFR end of similar near-infrared (NIR)-dark galaxy populations selected at higher radio frequencies reported in the literature. We performed a UV-to-radio median stacking analysis, dividing the sources with LOFAR ILT imaging according to the presence of radio excess. Both sub-samples are detected in the H _E band at 3σ and 9σ for the radio-excess and non–radio-excess sources, respectively. The two stacked populations exhibit similar global physical properties and differ primarily in their radio emission, with values consistent with those observed for individual sources, albeit with less extreme SFRs. These preliminary results indicate that, compared to similar selections carried out over smaller fields, the wide area covered by Euclid enables the identification of a higher fraction of systems in which intense star formation and AGN activity coexist, likely capturing a key phase of galaxy–black hole co-evolution.

We model intrinsic alignment (IA) in Euclid ’s Flagship simulation to investigate its impact on Euclid ’s weak lensing signal. Our IA implementation in the Flagship simulation takes the photometric properties of galaxies into account, along with their dark matter host halos. The simulation parameters are calibrated using combined constraints from observations and cosmological hydrodynamical simulations. We compare simulations against theory predictions, determining the parameters of two of the most widely used IA models: the nonlinear alignment (NLA) and the tidal alignment and tidal torquing (TATT) models. We measured the amplitude of the simulated IA signal as a function of galaxy magnitude and colour in the redshift range 0.1 < z < 2.1, close that of Euclid ’s main galaxy sample. We find that both NLA and TATT are able to accurately describe the IA signal in the simulation down to scales of 6–7 h ⁻¹ Mpc. We measured the alignment amplitudes for red galaxies that are comparable to those of the observations, using samples that had not been used in the initial calibration procedure. For blue galaxies, our constraints are consistent with zero alignments in our first redshift bin 0.1 < z < 0.3, but we detected a non-negligible signal at higher redshift; however, this signal is consistent with the upper limits set by observational constraints. Additionally, several hydrodynamical simulations have predicted alignments for spiral galaxies, in agreement with our findings. Finally, the evolution of alignment with redshift is realistic and comparable to what has been determined based on 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 improved agreement can be obtained when the 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 Euclid satellite will deliver a catalogue of optically selected galaxy clusters spanning from around 2000 deg ² in Data Release (DR) 1 to around 14 000 deg ² in DR3. In this work, we assess the validity of cluster clustering (CC) models for template-fitting, which complements the full-shape methodology by providing cosmological information from the anisotropy of the redshift-space two-point correlation function (2PCF). Both methods will be used to analyse the cluster 2PCF multipoles with Euclid . We examined the multipoles of the two-point redshift-space clustering of galaxy clusters simulated with the semi-analytic PINOCCHIO code using third-order Lagrangian perturbation theory, assuming a Euclid DR1-like footprint of 500 deg ² in the northern hemisphere and 1400 deg ² in the southern hemisphere. We estimated the first three even multipoles of the 2PCF and associated covariance matrix from 1000 DR1-like synthetic catalogues. We studied the impact of modelling the relevant non-linearities, halo bias, and photometric redshift uncertainties on the 2PCF. We applied three clustering models to the mock catalogues at 0 < z < 2 and with a virial mass of M _vir > 10 ¹⁴ h ⁻¹ M _⊙ under realistic and optimistic photometric redshift uncertainty scenarios. We formulated a set of permissive and conservative criteria that ought to be fulfilled by the multipole cut-off scales and validated them against 100 mock catalogues via an inference of the growth rate multiplied by the matter power spectrum normalisation parameter, fσ ₈ . We tested the dispersion, Scoccimarro, and Taruya–Nishimichi–Saito models. We find that the simplest of the three (i.e. the dispersion model) yields unbiased inferences on fσ ₈ from CC down to 10 h ⁻¹ Mpc in a DR1-like setting. All clustering models provide very similar goodness-of-fit metrics in the presence of DR1-like cluster redshift uncertainties.

Context. The Euclid mission has the potential to determine the fundamental physical nature of late-time cosmic acceleration and, as such, of deviations from the standard cosmological model, Λ cold dark matter. In this paper we focus on model-independent methods for modifying the evolution of scalar perturbations on linear scales. We considered two powerful and convenient approaches: The first is based on the two phenomenological modified gravity (PMG) parameters, μ _mg and Σ _mg , which are phenomenologically connected to the clustering of matter and weak lensing (WL), respectively. The second is the effective field theory (EFT) of dark energy and modified gravity, which we used to parameterise the braiding function, α _B , which defines the mixing between the metric and the dark energy field typical of Galileon theories. Aims. We estimate cosmological parameters based on spectroscopic and photometric primary probes by Euclid for a given set of additional parameters using the PMG and EFT models. Methods. We used the Fisher matrix method applied to spectroscopic galaxy clustering, WL, photometric galaxy clustering (GC _ph ), and the cross-correlation between GC _ph and WL. To model photometric predictions on nonlinear scales, we used the halo model reaction approach to cover two limiting cases for the screening mechanism: the unscreened (US) case, for which the screening mechanism is not present; and the super-screened (SS) case, which assumes strong screening. We also assumed scale cuts to account for our uncertainties when modelling nonlinear perturbation evolution. We chose a time-dependent form for { μ _mg , Σ _mg }, with two fiducial sets of values for the corresponding model parameters at the present time, { μ ¯ ₀ ,Σ¯ ₀ }, and two forms for α _B , with one fiducial set of values for each of the model parameters, α _B, 0 and { α _B, 0 , m }. Results. At the 68.3% confidence level, the percentage relative errors obtained with Euclid alone and our conservative settings for the full combination of probes for the US case are: for { μ ¯ ₀ ,Σ¯ ₀ }, with a ΛCDM fiducial, we obtain {23.3%, 2.6%}; for a fiducial { μ ¯ ₀ ,Σ¯ ₀ } = {0.5,0.5} we obtain {36.2%, 2.7%}; for α _B, 0 whose fiducial is 0.2, we have 31.1%; and for { α _B, 0 , m } with fiducial {0.9, 2.4} we have 11.6% and 11.8%. The constraints we obtain with the SS prescription provide similar values. We also computed constraints for different combinations of probes to assess their standalone and complementary constraining power.

Weak lensing surveys require accurate an correction for the point spread function (PSF) when measuring galaxy shapes. For a diffraction-limited PSF, which arises in the context of space-based missions, this correction depends on each galaxy’s spectral energy distribution (SED). Therefore, sufficiently accurate knowledge of the SED is needed for every galaxy. In the Euclid mission, galaxy SED reconstruction, which is one of the tasks of the photometric-redshift processing function (PHZ PF), relies on broad- and medium-band ancillary photometry. The limited wavelength sampling of the I _E passband and signal-to-noise ratio might affect the reconstruction accuracy and translate into biases in the weak lensing measurements. In this study, we present the methodology employed in the Euclid PHZ PF for reconstructing galaxy SEDs at 55 wavelengths, sampling the I _E passband every 10 nm, and we assess whether it fulfils the accuracy requirements imposed on the Euclid PSF model. We employed both physics- and data-driven methods, focussing on a new approach of template-based flux correction and Gaussian processes. For validation, we introduced an SED metric whose bias translates into inaccuracies in the PSF quadrupole moments. 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 that leverages both methods. This solution proves effective in meeting the Euclid accuracy requirements for most of the redshift range of the survey. Finally, we investigated 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 I _E passband. This study offers 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 present an end-to-end, iterative pipeline for efficient identification of strong galaxy-galaxy lensing systems, applied to the Euclid Q1 imaging data. Starting from the VIS catalogues, we rejected point sources, applied a magnitude cut ( I _E ≤ 24) on the deflectors, and ran a pixel-level artefact-and-noise filter to build 96 × 96 pixel cutouts. The VIS+NISP colour composites were constructed with a VIS-anchored luminance scheme that preserves VIS morphology and NISP colour contrast. A VIS-only seed classifier supplies clear positives and typical impostors, which we used to curate a morphology-balanced negative set and augment scarce positives. Among the six compact convolutional neural networks (CNNs) that had been studied initially, the modified VGG16 (GlobalAveragePooling + 256/128 dense layers with the last nine layers trainable) exhibited the best performance. In our run, the training set grew from 27 seed lenses (augmented 67× to 1809) plus 2000 negatives to a colour dataset of 30 686 images. After three rounds of iterative fine-tuning, a human grading of the top 4000 candidates ranked by the final model yielded 441 Grade A/B candidate lensing systems, including 311 overlapping with the existing Q1 strong-lens catalogue, and 130 additional A/B candidates (9 As and 121 Bs) not previously reported. Independently, the model recovered 740 out of 905 (81.8%) candidate Q1 lenses within its top 20 000 predictions, considering off-centred samples. Candidates span I _E ≃ 17–24 AB mag (median 21.3 AB mag) and are redder in Y _E − H _E than the parent population, consistent with massive early-type deflectors. Each training iteration required about a week for a small team and the approach can easily be scaled to future wide-area Euclid releases. Subsequent works will focus on calibrating the selection function via lens injection, extending recall through uncertainty-aware active learning, and exploring multi-scale or attention-based neural networks with fast post hoc vetters that incorporate lens models into the classification.