Luca Valenziano

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.

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.

Aims. In this paper we present cosmological parameter forecasts for the Euclid 6 × 2 pt statistics, which include the galaxy clustering and weak lensing main probes together with previously neglected cross-covariance and cross-correlation signals between imaging-photometric and spectroscopic data. The aim is understanding the impact of such cross-terms on the expected Euclid performance. Methods. We adopted the Fisher information matrix approach to produce 6 × 2 pt cosmological forecasts from Euclid , considering two different techniques known as the harmonic and hybrid approaches, respectively. In the first, we treat all the different Euclid probes in the same way, i.e., we consider only angular 2 pt statistics for spectroscopic and photometric galaxy distributions, as well as for weak lensing, fully analyzing all their possible cross-covariances and cross-correlations in the spherical harmonic domain. In the second, thanks to lessons learned from the harmonic approach, we do not account for negligible cross-covariances between the 3D spectroscopic galaxy distribution and the 2D photometric/imaging data, but consider the combination of their cross-correlation with the autocorrelation signals. Results. We find that both cross-covariance and cross-correlation signals between the two Euclid main probes, i.e., the spectroscopic galaxy sample and the photometric-imaging data, have a negligible impact on the cosmological parameter constraints and therefore on the Euclid performance. In the case of the hybrid approach, we attribute this result to the effect of the cross-correlation between weak lensing and photometric data, which is dominant with respect to other cross-correlation signals, and to the better performance of the full anisotropic 3D spectroscopic galaxy clustering with respect to the projected clustering. In the case of the 2D harmonic approach, we attribute this result to two main theoretical limitations of the 2D projected statistics implemented in this work according to the analysis of the official Euclid forecasts: the high shot noise and the limited redshift range of the spectroscopic sample, with respect to the photometric sample, together with the suppression of radial information from subdominant contributions such as redshift-space distortions and lensing magnification. Therefore, our analysis suggests that 2D and 3D Euclid data can be safely treated as independent, with a great saving in computational resources.

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 investigated the pixel-to-pixel noise correlations of HAWAII-2RG (H2RG) detectors using data from preflight testing performed for Euclid . We find that the detectors – in the absence of input signal, with and without the focal plane electronics that will be used on board Euclid – carry pixel-to-pixel noise correlations with varying amplitude across our sample of 23 detectors. We find a baseline level of order 10%, but with variations among detectors and portions of a given detector. We also observe occasional, significantly higher levels, which we attribute to fluctuations in alternative column noise. These fluctuations affect approximately a tenth of the total number of exposures and result in Pearson correlation coefficient values as high as 40% for the worst cases. While our sample of detectors is specific to Euclid , we expect our results to apply in general to the family of H2RG detectors, widely used in infrared astronomy.

The large-scale structure (LSS) of the Universe is an important probe for deviations from the canonical cosmological constant Λ and cold dark matter (ΛCDM) model. A statistically significant detection of any deviations would signify the presence of a new physics or the breakdown of any number of the underlying assumptions of the standard cosmological model or possible systematic errors in the data. In this paper, we quantify the ability of the LSS data products of the spectroscopic survey of the Euclid mission, together with other contemporary surveys, to improve the constraints on deviations from ΛCDM in the redshift range 0 < z < 1.75. We consider both currently available growth rate data and simulated data with specifications from Euclid and external surveys, based on ΛCDM and a modified gravity (MoG) model with an evolving Newton’s constant (denoted μCDM), and carry out a binning method and a machine learning reconstruction, based on genetic algorithms (GAs), of several LSS null tests. Using the forecast Euclid growth data from the spectroscopic survey in the range 0.95 < z < 1.75, we find that in combination with external data products (covering the range 0 < z < 0.95), Euclid will be able to improve the precision of current null tests of the LSS on average by a factor of eight when using a binning method and a factor of six when using the GAs. Our work highlights the need for synergies between Euclid and other surveys, but also the usefulness of statistical analyses, such as GAs, in order to disentangle any degeneracies in the cosmological parameters. Both are necessary to provide tight constraints over an extended redshift range and to probe for deviations from the ΛCDM model.

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.

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.

The large catalogues of galaxy clusters expected from the Euclid survey will enable cosmological analyses of cluster number counts that require accurate cosmological model predictions. One possibility is to use parametric fits calibrated against N -body simulations, which capture the cosmological parameter dependence of the halo mass function (HMF). Several studies have shown that this can be obtained through a calibration against haloes with spherical masses defined at the virial overdensity. In contrast, if different mass definitions are used for the HMF and the mass-observable relation, a mapping between them is required. Here, we investigate the impact of such a mapping on the cosmological parameter constraints inferred from galaxy cluster number counts for a fiducial Λ cold dark matter cosmology. Using synthetic data from N -body simulations, we show that the standard approach, which relies on assuming a concentration-mass relation, can introduce significant systematic bias. In particular, depending on the halo mass definition and the concentration-mass relation assumed, this can lead to biased constraints at a level of more than 2 σ . In contrast, we find that in all the cases we have considered, the mass conversion based on the halo sparsity statistics results in a systematic bias that is smaller than the statistical error.