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 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 (≲3 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.

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 H0 and the matter clustering amplitude σ8, 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 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.

Radiation pressure from Lyman-α (Lyα) scattering is a potentially dominant form of early stellar feedback, capable of injecting up to ∼ 100 × more momentum into the interstellar medium (ISM) than ultraviolet continuum radiation pressure and stellar winds. Lyα feedback is particularly strong in dust-poor environments and is thus especially important during the formation of the first stars and galaxies. As upcoming galaxy formation simulations incorporate Lyα feedback, it is crucial to consider processes that can limit it to avoid placing Lambda-cold dark matter in apparent tension with recent JWST observations indicating efficient star formation at Cosmic Dawn. We study Lyα feedback using a novel analytical Lyα radiative transfer solution that includes the effects of continuum absorption, gas velocity gradients, Lyα destruction (e.g. by 2p → 2s transitions), ISM turbulence, and atomic recoil. We verify our solution for uniform clouds using extensive Monte Carlo radiative transfer (MCRT) tests, and resolve a previous discrepancy between analytical and MCRT predictions. We then study the sensitivity of Lyα feedback to the aforementioned effects. While these can dampen Lyα feedback by a factor ≤ few × 10, we find it remains ≥ 5 − 100 × stronger than direct radiation pressure and therefore cannot be neglected. We provide an accurate fit for the Lyα force multiplier MF, suitable for implementation in subgrid models for galaxy formation simulations. Our findings highlight the critical role of Lyα feedback in regulating star formation at Cosmic Dawn, and underscore the necessity of incorporating it into simulations to accurately model early galaxy evolution.

We present and analyse the results of the Science Data Challenge 3a (SDC3a, https://sdc3.skao.int/challenges/foregrounds), an epoch of reionization (EoR) foreground-removal exercise organized by the Square Kilometre Array Observatory (SKAO) on SKA simulated data. The challenge ran for 8 months, from 2023 March to October. Participants were provided with realistic simulations of SKA-Low data between 106 and 196 MHz, including foreground contamination from extragalactic and Galactic emission, instrumental, and systematic effects. They were asked to deliver cylindrical power spectra of the EoR signal, cleaned from all corruptions, and the corresponding confidence levels. Here, we describe the approaches taken by the 17 teams that completed the challenge, and we assess their performance using different metrics. The challenge results provide a positive outlook on the capabilities of current foreground-mitigation approaches to recover the faint EoR signal from SKA-Low observations. The median error committed in the EoR power spectrum recovery is below the true signal for seven teams, although in some cases, there are some significant outliers. The smallest residual overall is 4.2+−4202 × 10−4 K2h−3cMpc3 across all considered scales and frequencies. The estimation of confidence levels provided by the teams is overall less accurate, with the true error being typically underestimated, sometimes very significantly. The most accurate error bars account for 60 ± 20 per cent of the true errors committed. The challenge results provide a means for all teams to understand and improve their performance. This challenge indicates that the comparison between independent pipelines could be a powerful tool to assess residual biases and improve error estimation.

The final stages of cosmic reionization (EndEoR) are expected to be strongly regulated by the residual neutral hydrogen in the already ionized regions of the Universe. Its presence limits the mean distance that ionizing photons can travel and hence the extent of the regions that sources of ionizing photons can affect. The structures containing most of this residual neutral hydrogen are typically unresolved in large-scale simulations of reionization. Here, we investigate and compare a range of approaches for including the effect of these small-scale absorbers, also known as Lyman limit systems (LLSs), in such simulations. We evaluate the impact of these different approaches on the reionization history, the evolution of the ultraviolet background, and its fluctuations. We also compare to observational results on the distribution of Lyman-α opacity towards the EndEoR and the measured mean free path of ionizing photons. We further consider their effect on the 21-cm power spectrum. We find that although each of the different approaches can match some of the observed probes of the final stages of reionization, only the use of a redshift-dependent and position-dependent LLS model is able to reproduce all of them. We therefore recommend that large-scale reionization simulations, which aim to describe both the state of the ionized and neutral intergalactic medium, use such an approach, although the other, simpler approaches are applicable depending on the science goal of the simulation.

In recent years, a Gaussian process regression (GPR)-based framework has been developed for foreground mitigation from data collected by the LOw-Frequency ARray (LOFAR), to measure the 21-cm signal power spectrum from the Epoch of Reionization (EoR) and cosmic dawn. However, it has been noted that through this method there can be a significant amount of signal loss if the EoR signal covariance is misestimated. To obtain better covariance models, we propose to use a kernel trained on the GRIZZLY simulations using a Variational Auto-Encoder (VAE)-based algorithm. In this work, we explore the abilities of this machine learning-based kernel (VAE kernel) used with GPR, by testing it on mock signals from a variety of simulations, exploring noise levels corresponding to ≈10 nights (≈141 h) and ≈100 nights (≈1410 h) of observations with LOFAR. Our work suggests the possibility of successful extraction of the 21-cm signal within 2σ uncertainty in most cases using the VAE kernel, with better recovery of both shape and power than with previously used covariance models. We also explore the role of the excess noise component identified in past applications of GPR and additionally analyse the possibility of redshift dependence on the performance of the VAE kernel. The latter allows us to prepare for future LOFAR observations at a range of redshifts, as well as compare with results from other telescopes.