Hydrogen is the most abundant element in our Universe. The first generation of stars and galaxies produced photons that ionized hydrogen gas, driving a cosmological event known as the Epoch of Reionization (EoR). The upcoming Square Kilometre Array Observatory (SKAO) will map the distribution of neutral hydrogen during this era, aiding in the study of the properties of these first-generation objects. Extracting astrophysical information will be challenging, as SKAO will produce a tremendous amount of data where the hydrogen signal will be contaminated with undesired foreground contamination and instrumental systematics. To address this, we develop some of the latest deep learning techniques to extract information from the 2D power spectra of the hydrogen signal expected from SKAO. We apply a series of neural network models to these measurements and quantify their ability to predict the history of cosmic hydrogen reionization, which is connected to the increasing number and efficiency of early photon sources. We show that the study of the early Universe benefits from modern deep learning technology. In particular, we demonstrate that dedicated machine learning algorithms can achieve more than a 0.95 R² score on average in recovering the reionization history. This enables accurate and precise cosmological and astrophysical inference of structure formation in the early Universe.

The reionization of the intergalactic medium (IGM) was driven by the first stars, galaxies, and accreting black holes. However, the relative importance of these sources and the efficiency by which ionizing photons escape into the IGM remain poorly understood. Most reionization modelling frameworks assume idealized, isotropic emissions. We investigate this assumption by examining a suite of simulations incorporating directed, anisotropic photon emissions. We find that such anisotropic emissions of ionizing photons yield a different reionization geometry compared to the standard, isotropic, case. During the early stages of reionization (when less than 30 per cent of the Universe is ionized), simulations with narrow photon leakage channels produce smaller ionized bubbles on average. However, these bubbles grow to similar sizes during the middle stages of reionization. This anisotropy not only produces a distinctive evolution of the size distribution of the ionized regions, but also imprints a feature onto the spherically averaged power spectra of the 21-cm signal throughout reionization. We observe a suppression in power by about 10–40 per cent at scales corresponding to wavenumbers k = 0.1-1 h Mpc-1, corresponding to the range in which current radio interferometers are most likely to measure the power spectrum. The simulation with the narrowest channel of ionization emission shows the strongest suppression. However, this anisotropic emission process does not introduce any measurable anisotropy in the 21-cm signal. 

The power spectra of the redshifted 21 cm signal from the Epoch of Reionization (EoR) contain information about the ionization and thermal states of the intergalactic medium (IGM) and depend on the properties of the sources that existed during that period. Recently, the LOFAR-EoR Key Science Project team has analysed ten nights of LOFAR high-band data and estimated upper limits on the 21 cm power spectrum at redshifts 8.3, 9.1, and 10.1. Here, we used these upper limit results to constrain the properties of the IGM at those redshifts. We focus on the properties of the ionized and heated regions where the temperature is larger than that of the cosmic microwave background (CMB). We modelled the power spectrum of the 21 cm signal with the code GRIZZLY and used a Bayesian inference framework to explore the source parameters for uniform priors on their ranges. The framework also provides information about the IGM properties in the form of derived parameters. We do not include constraints from other observables except for some very conservative limits on the maximum ionization fraction at those redshifts, which we estimated from the CMB Thomson scattering optical depth. In a model that includes a radio background in excess of the CMB, the 95% (68%) credible intervals of disfavoured models at redshift 9.1 for the chosen priors correspond to IGM states with an averaged ionization and heated fraction below 0.46 (≤ 0.05), an average gas temperature below 44 K (4 K), and a characteristic size of the heated region of ≤ 14 h^-1 Mpc (≤ h^-1 Mpc). The 68% credible interval suggests an excess radio background that is more than 100% of the CMB at 1.42 GHz, while the 95% credible interval of the radio background efficiency parameter spans the entire prior range. The behaviour of the credible intervals is similar at all redshifts. The models disfavoured by the LOFAR upper limits are extreme, as they are mainly driven by rare and large ionized or heated regions. We find that the inclusion of upper limits from other radio interferometric observations in the Bayesian analysis significantly increases the number of disfavoured EoR models, thus enhancing the disfavoured credible intervals of the IGM parameters, especially those related to the average gas temperature and size distribution of the heated regions. While our constraints are not yet very strong, more stringent upcoming results from 21 cm observations together with the detection of many high-z galaxies, for example with the James Webb Space Telescope, will strengthen understanding of this crucial phase of the Universe.

The low-frequency component of the upcoming Square Kilometre Array Observatory (SKA-Low) will be sensitive enough to construct 3D tomographic images of the 21-cm signal distribution during reionization. However, foreground contamination poses challenges for detecting this signal, and image recovery will heavily rely on effective mitigation methods. We introduce SERENEt, a deep-learning framework designed to recover the 21-cm signal from SKA-Low's foreground-contaminated observations, enabling the detection of ionized (H ii) and neutral (H i) regions during reionization. SERENEt can recover the signal distribution with an average accuracy of 75 per cent at the early stages () and up to 90 per cent at the late stages of reionization (). Conversely, H i region detection starts at 92 per cent accuracy, decreasing to 73 per cent as reionization progresses. Beyond improving image recovery, SERENEt provides cylindrical power spectra with an average accuracy exceeding 93 per cent throughout the reionization period. We tested SERENEt on a 10-deg field-of-view simulation, consistently achieving better and more stable results when prior maps were provided. Notably, including prior information about H ii region locations improved 21-cm signal recovery by approximately 10 per cent. This capability was demonstrated by supplying SERENEt with ionizing source distribution measurements, showing that high-redshift galaxy surveys of similar observation fields can optimize foreground mitigation and enhance 21-cm image construction.

We present new upper limits on the 21 cm signal power spectrum from the epoch of reionisation (EoR), at redshifts z ∼ 10.1,9.1, and 8.3, based on reprocessed observations from the Low-Frequency Array (LOFAR). The analysis incorporates significant enhancements in calibration methods, sky model subtraction, radio-frequency interference (RFI) mitigation, and an improved signal separation technique using machine learning to develop a physically motivated covariance model for the 21 cm signal. These advancements have markedly reduced previously observed excess power due to residual systematics, bringing the measurements closer to the theoretical thermal noise limit across the entire k-space. Using comparable observational data, we achieve a two- to fourfold improvement over our previous LOFAR limits, with best upper limits of I 212 < (68.7 mK)2 at k=0.076 h cMpc1, I212 < (54.3 mK)2 at k=0.076 h cMpc 1, and I212 < (65.5a mK)2 at k=0.083 h cMpc 1 at redshifts z ∼ 10.1,9.1, and 8.3, respectively. These new multi-redshift upper limits provide new constraints that can be used to refine our understanding of the astrophysical processes during the EoR. Comprehensive validation tests, including signal injection, were performed to ensure the robustness of our methods. The remaining excess power is attributed to residual foreground emissions from distant sources, beam model inaccuracies, and low-level RFI. We discuss ongoing and future improvements to the data processing pipeline aimed at further reducing these residuals, thereby enhancing the sensitivity of LOFAR observations in the quest to detect the 21 cm signal from the EoR.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

The Euclid mission of the European Space Agency will provide weak gravitational lensing and galaxy clustering surveys that can be used to constrain the standard cosmological model and its extensions, with an opportunity to test the properties of dark matter beyond the minimal cold dark matter paradigm. We present forecasts from the combination of the Euclid weak lensing and photometric galaxy clustering data on the parameters describing four interesting and representative non-minimal dark matter models: a mixture of cold and warm dark matter relics; unstable dark matter decaying either into massless or massive relics; and dark matter undergoing feeble interactions with relativistic relics. We modelled these scenarios at the level of the non-linear matter power spectrum using emulators trained on dedicated N-body simulations. We used a mock Euclid likelihood and Monte Carlo Markov chains to fit mock data and infer error bars on dark matter parameters marginalised over other parameters. We find that the Euclid photometric probe (alone or in combination with cosmic microwave background data from the Planck satellite) will be sensitive to the effect of each of the four dark matter models considered here. The improvement will be particularly spectacular for decaying and interacting dark matter models. With Euclid, the bounds on some dark matter parameters can improve by up to two orders of magnitude compared to current limits. We discuss the dependence of predicted uncertainties on different assumptions: the inclusion of photometric galaxy clustering data, the minimum angular scale taken into account, and modelling of baryonic feedback effects. We conclude that the Euclid mission will be able to measure quantities related to the dark sector of particle physics with unprecedented sensitivity. This will provide important information for model building in high-energy physics. Any hint of a deviation from the minimal cold dark matter paradigm would have profound implications for cosmology and particle physics.

A detection of the 21-cm signal power spectrum from the Epoch of Reionization is imminent, thanks to consistent advancements from telescopes such as LOFAR, MWA, and HERA, along with the development of SKA. In light of this progress, it is crucial to expand the parameter space of simulations used to infer astrophysical properties from this signal. In this work, we explore the role of cosmological parameters such as the Hubble constant H<inf>0</inf> and the matter clustering amplitude σ<inf>8</inf>, whose values as provided by measurements at different redshifts are in tension. We run N-body simulations using gadget-4, and post-process them with the reionization simulation code polar, that uses L-Galaxies to include galaxy formation and evolution properties and grizzly to execute 1D radiative transfer of ionizing photons in the intergalactic medium (IGM). We compare our results with the latest James Webb Space Telescope (JWST) observations and explore which astrophysical properties for different cosmologies are necessary to match the observed UV luminosity functions at redshifts z = 10 and 9. Additionally, we explore the impact of these parameters on the observed 21-cm signal power spectrum upper limits, focusing on the redshifts within the range of LOFAR 21-cm signal observations (z ≈ 8.5-10). Despite differences in cosmological and astrophysical parameters, our models cannot be ruled out by the current upper limits. This suggests the need for broader physical parameter spaces for inference modeling to account for all models that agree with observations. However, we also propose stronger constraining power by using a combination of galactic and IGM observables.

The redshifted 21-cm signal of neutral hydrogen from the epoch of reionization (EoR) can potentially be detected using lowfrequency radio instruments such as the Low-Frequency Array (LOFAR). So far, LOFAR upper limits on the 21-cm signal power spectrum have been published using a single target field: the North Celestial Pole (NCP). In this work, we analyse and provide upper limits for the 3C 196 field, observed by LOFAR, with a strong ≈80 Jy source in the centre. This field offers advantages such as higher sensitivity due to zenith-crossing observations and reduced geostationary radio-frequency interference, but also poses challenges due to the presence of the bright central source. After constructing a wide-field sky model, we process a single 6-h night of 3C 196 observations using direction-independent and direction-dependent calibration, followed by a residual foreground subtraction with a machine learning Gaussian processregression (ML-GPR). A bias correction is necessary to account for signal suppression in the GPR step. Still, even after this correction, the upper limits are a factor of 2 lower than previous single-night NCP results, with a lowest 2σ upper limit of (146.61 mK) ²at redshift z = 9.16 and wavenumber k = 0.078 h cMpc⁻¹ (with dk/k ≈ 0.3). The results also reveal an excess power, different in behaviour from that observed in the NCP field, suggesting a potential residual foreground origin. In future work, the use of multiple nights of 3C 196 observations combined with improvements to sky modelling and ML-GPR to avoid the need for bias correction should provide tighter constraints per unit observing time than the NCP.

The high redshift 21-cm signal promises to be a crucial probe of the state of the intergalactic medium (IGM). Understanding the connection between the observed 21-cm power spectrum and the physical quantities intricately associated with the IGM is crucial to fully understand the evolution of our Universe. In this study, we develop an emulator using artificial neural network (ANN) to predict the 21-cm power spectrum from a given set of IGM properties, namely, the bubble size distribution and the volume averaged ionization fraction. This emulator is implemented within a standard Bayesian framework to constrain the IGM parameters from a given 21-cm power spectrum. We compare the performance of the Bayesian method to an alternate method using ANN to predict the IGM parameters from a given input power spectrum, and find that both methods yield similar levels of accuracy, while the ANN is significantly faster. We also use this ANN method of parameter estimation to predict the IGM parameters from a test set contaminated with noise levels expected from the SKA-LOW instrument after 1000 hours of observation. Finally, we train a separate ANN to predict the source parameters from the IGM parameters directly, at a redshift of z = 9.1, demonstrating the possibility of a non-analytic inference of the source parameters from the IGM parameters for the first time. We achieve high accuracies, with R2-scores ranging between 0.898-0.978 for the ANN emulator and between 0.966-0.986 and 0.817-0.981 for the predictions of IGM parameters from 21-cm power spectrum and source parameters from IGM parameters, respectively. The predictions of the IGM parameters from the Bayesian method incorporating the ANN emulator leads to tight constraints on the IGM parameters.