Henk Hoekstra

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.

We present the discovery of two disky titans in the first data release of the Euclid satellite. These sources are massive ( M _* > 10 ¹¹ M _⊙ ) star-forming (SFR ∼ 20 M _⊙ yr ⁻¹ ) disks located in strong over-dense environments at intermediate redshifts ( z ∼ 0.75). They represent a small fraction of the massive galaxies in over-dense regions (just four candidates in over 20 deg ² analysed in this study). Their existence is puzzling, given the abundance of passive, bulge-dominated sources commonly found at the centre of groups and clusters at low redshifts. First, our analysis shows that these objects are located in massive groups ( M _h ∼ 10 ^13.8 M _⊙ ), where rapid accretion of cold gas should be prevented by the formation of a static hot halo. Despite this, a millimetre follow-up with NOEMA shows significant cold gas reservoirs ( M H ₂ ∼ 10 ^10.3 M _⊙ ) within these sources. Second, our morphological analysis indicates a massive, passive bulge in these galaxies. This bulge is expected to stabilise the disk against fragmentation, thereby suppressing further star formation. However, these sources lie on the Schmidt–Kennicutt relation or even slightly above. Building on these observations, we propose a scenario where these disky titans are the product of a merger-induced rejuvenation episode, in which the most massive galaxy in a group accretes cold gas from another member and briefly restarts star formation. Such a scenario is supported by a comparison with the TNG300 simulation and easily explains the persistence of star formation activity in massive galaxies in over-dense environments as temporary stages of more complex evolution. More generally, our study showcases the ability of Euclid to find rare objects, thanks to the unprecedented statistic offered by its surveys and the scientific potential residing in the synergy between Euclid and other facilities observing at longer wavelengths.

A number of cosmic shear studies have reported results that are in mild tension with Planck cosmic microwave background measurements. To explore if this can be caused by biases in shear estimation, we revisit data analyses from the Kilo-Degree Survey (KiDS) using an alternative shape measurement pipeline that is more robust to uncertainties in the calibration. To this end, we present an implementation of M ETA C ALIBRATION and compare its performance to that of lens fit, which has been used in previous data analyses. We find that the multiplicative bias is reduced, in particular for the most distant redshifts, as derived from multi-band image simulations designed to match the KiDS data. For all tomographic bins, we obtain a multiplicative bias | m |< 0.017, with negligible additive bias. Importantly, the calibration has a negligible sensitivity to key galaxy properties. The resulting robust shear estimates were used to obtain cosmological parameter constraints. We find that the parameter, S ₈ ≡ √ σ ₈ Ω _m /0.3 = 0.789 _−0.024 ^+0.020 , is consistent with the previous KiDS-1000 lens fit constraint of S ₈ = 0.776 ^+0.029+0.002 _{−0.027−0.003} (statistical and systematic errors). Thanks to the higher effective source density of the M ETA C ALIBRATION catalogue, the constraining power is improved by about 28%. The difference in S ₈ with the Planck value remains at a similar level (1.8 σ ), implying that it is not caused by the shear measurements.

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.

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 report the first detection of the ‘convective-transition gap’ (also known as the ‘M-dwarf gap’) in the globular cluster 47 Tuc (NGC 104). This feature, linked to a change in the physical properties of late-type dwarfs, has remained elusive, with only two detections so far. Leveraging the large number of stars, high resolution, and photometric precision enabled by Euclid , we detected a statistically significant, sharp discontinuity in the main-sequence luminosity function of 47 Tuc at I _E ≈22.9, which we identify as the convective-transition gap. A comparison of the observed properties of the gap in 47 Tuc with theoretical models shows how the gap can be a powerful diagnostic for probing the internal chemical structure of globular clusters and their multiple stellar populations. Following its initial discovery in the metal-poor cluster NGC 6397, the identification of a convective gap in the metal-rich 47 Tuc suggests that this feature is more general than previously thought. These results demonstrate that Euclid can be transformative well beyond cosmology, with impacts across multiple areas of astrophysics, including resolved stellar populations.

The intrinsic alignments of galaxies are a potentially major contaminant among cosmological analyses of weak gravitational lensing. In this work, we constructed a semi-analytic model of galaxy ellipticities and alignments in the Euclid Flagship simulation to predict this contamination in Euclid ’s weak lensing observations. Galaxy shapes and orientations were determined by the corresponding properties of the host haloes in the underlying N -body simulation, as well as the relative positions of galaxies within their halo. Alignment strengths were moderated via stochastic misalignments, separately for central and satellite galaxies, and were dependent on the galaxy’s redshift, luminosity, and rest-frame colour. The resulting model was calibrated against galaxy ellipticity statistics from the COSMOS Survey, selected alignment measurements based on Sloan Digital Sky Survey samples, and galaxy orientations extracted from the Horizon-AGN hydrodynamic simulation at redshift z = 1. The best-fit model has a total of 12 alignment parameters and generally reproduces the calibration data sets well within the 1 σ statistical uncertainties of the observations and the Flagship simulation, with notable exceptions for the most luminous subsamples on small physical scales. The statistical power of the calibration data and the volume of the single Flagship realisation are still too small to provide informative prior ranges for intrinsic alignment amplitudes in relevant galaxy samples. Given these uncertainties, we predict that Euclid end-of-mission tomographic weak gravitational lensing two-point statistics will end up modified due to intrinsic alignments, by up to 10%.

We report the discovery of 31 new high- z quasars in the redshift range 6.6 < z < 7.8. These quasars were selected from approximately 3000 deg ² of sky covered during the first 1.5 years of the Euclid Wide Survey, representing the initial results of the Euclid high- z quasar search. Our candidate selection employed multiple machine-learning and probabilistic techniques applied to the EuclidI _E , Y _E , J _E , and H _E images, supplemented by ancillary z -band data when available. Spectroscopic follow-up observations were carried out with Keck, Magellan, and the Large Binocular Telescope (LBT). Among the new discoveries, there are 12 quasars at z ≥ 7, more than doubling the number of previously known quasars at z ≥ 7. The newly discovered quasars exhibit 21.2 < J _E < 23.2 (−25.5 < M ₁₄₅₀ < −23.6), extending quasar studies to the faint end of the quasar luminosity function (QLF) at z ≳ 7. The quasar with the highest- z , EUCL J172902.75+641018.1 at z ≈ 7.77, sets the new redshift record for the most distant quasar ever reported. These discoveries demonstrate Euclid ’s transformative role in high- z quasar discovery and set the stage for future follow-up studies of the early galaxies hosting quasars, supermassive black hole growth, and the intergalactic medium in the epoch of reionisation.