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 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.

During the Epoch of Reionization (EoR), the ultraviolet radiation from the first stars and galaxies ionized the neutral hydrogen of the intergalactic medium, which can emit radiation through its 21 cm hyperfine transition. Measuring the 21 cm power spectrum is a key science goal for the future Square Kilometre Array (SKA); however, observing and interpreting it is a challenging task. Another high-potential probe of the EoR is the patchy kinetic Sunyaev–Zel’dovich (pkSZ) effect, observed as a foreground to the cosmic microwave background temperature anisotropies on small scales. Despite recent promising measurements, placing constraints on reionization from pkSZ observations is a non-trivial task, subject to strong model dependence. We propose to alleviate the difficulties in observing and interpreting the 21 cm and pkSZ power spectra by combining them. With a simple yet effective parametric model that establishes a formal connection between them, we can jointly fit mock 21 cm and pkSZ data points. We confirm that these observables provide complementary information on reionization, leading to significantly improved constraints when combined. We demonstrate that with as few as two measurements of the 21 cm power spectrum with 100 h of observations with the SKA, as well as a single ℓ = 3000 pkSZ data point, we can reconstruct the reionization history of the universe and its morphology. We find that the reionization history (morphology) is better constrained with two 21 cm measurements at different redshifts (scales). Therefore, a combined analysis of the two probes will give access to tighter constraints on cosmic reionization even in the early stages of 21 cm detections.

We apply the inverse Gertsenshtein effect, i.e., the graviton-photon conversion in the presence of a magnetic field, to constrain high-frequency gravitational waves (HFGWs). Using existing astrophysical measurements, we compute upper limits on the GW energy densities Ω_GW at 16 different frequency bands. Given the observed magnetisation of galaxy clusters with field strength B ∼ μG correlated on (10) kpc scales, we estimate HFGW constraints in the (10²) GHz regime to be Ω_GW ≲ 10¹⁶ with the temperature measurements of the Atacama Cosmology Telescope (ACT). Similarly, we conservatively obtain Ω_GW ≲ 10¹³ (10¹¹) in the (10²) MHz ((10) GHz) regime by assuming uniform magnetic field with strength B ∼ 0.1 nG and saturating the excess signal over the Cosmic Microwave Background (CMB) reported by radio telescopes such as the Experiment to Detect the Global EoR Signature (EDGES), LOw Frequency ARray (LOFAR), and Murchison Widefield Array (MWA), and the balloon-borne second generation Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission (ARCADE2) with graviton-induced photons. The upcoming Square Kilometer Array (SKA) can tighten these constraints by roughly 10 orders of magnitude, which will be a step closer to reaching the critical value of Ω_GW = 1 or the Big Bang Nucleosynthesis (BBN) bound of Ω_GW ≃ 1.2 × 10^-6. We point to future improvement of the SKA forecast and estimate that proposed CMB measurement at the level of (10^0-2) nK, such as Primordial Inflation Explorer (PIXIE) and Voyage 2050, are needed to viably detect stochastic backgrounds of HFGWs.

The first billion years of the Universe is a unique era, marked by the formation of the first stars, galaxies, and accreting black holes, which release ionising radiation into the intergalactic medium (IGM). As a result, these luminous sources initiate a period during which the cold and dense IGM, primarily consisting of neutral hydrogen (H_I), is heated and ionised. We refer to this era as the Epoch of Reionization (EoR). The EoR is a global phase transition that is not trivial to observe or model computationally. It is a multi-scale event that evolves with time and depends on the nature of the astrophysical processes that govern the formation of stars and galaxies, as well as the fundamental cosmology that defines the properties of the large-scale IGM. While various measurements of cosmic reionization exist, presently they are too few to constrain the entirety of the process. However, observations from the James Webb Space Telescope and the Square Kilometre Array (SKA), among others, will provide new insight into the process. Particularly, the SKA will observe the power spectrum (PS) of the 21 cm signal from the EoR, which originates from the hyperfine transition of neutral hydrogen atoms H_I in the IGM that can emit 21 cm photons. 

In Paper I, we investigate the evolution of the 21 cm PS across the EoR by perturbing the signal and studying its composing terms. We highlight the importance higher-order terms play in shaping the PS on large scales and quantify its evolution. Crucially, we find a characteristic length scale within the 21 cm PS, determined by the mean free path ionising photons travel in the IGM (MFP). Hence, the 21 cm PS has two regimes. We show that the large-scale signal is a biased version of the cosmological density field, and the small-scale PS is determined by the astrophysics of reionization. In Paper II, we use the decomposition of the 21 cm PS and relate it to the PS of the free electron density field. Thus, we analytically connect the 21 cm observable to a probe of the free electron density field. Such a probe is the patchy kinetic Sunyaev-Zel'dovich effect (pkSZ), observed as a foreground to the primary cosmic microwave background temperature anisotropies on small scales. The pkSZ is an integrated probe sensitive to the duration of the EoR and the characteristic size of ionised bubbles. We construct a forecast study of both probes. We show that inferences from 21 cm PS from the SKA can be verified when combined with the pkSZ observation, as each data set is influenced by different systematics. In Paper III, we focus on the modelling of the MFP within large-scale simulations, focusing on the end of reionization (EndEoR). The MFP of ionising photons is inferred from quasar data and depends on several factors. In the post-EoR era, it depends on the distribution and evolution of Lyman Limit systems (LLS), small-scale absorbers that are typically not resolved in large-scale simulations. We investigate the assumptions needed to accurately model the LLS in simulations, and we study their impact on the observables at the EndEoR. We find that LLS modelling has a profound impact on the duration of the final stages of the EoR, the shape of the 21 cm PS as well as other observables of the ionised IGM inferred from quasar spectra, such as the Ultraviolet Background of ionising photons, the effective optical depth of Lyman alpha photons, and the MFP of ionising photons.

Radio interferometers, such as the Low-Frequency Array and the future Square Kilometre Array, are attempting to measure the spherically averaged 21-cm power spectrum from the epoch of reionization. Understanding of the dominant physical processes which influence the power spectrum at each length-scale is therefore crucial for interpreting any future detection. We study a decomposition of the 21-cm power spectrum and quantify the evolution of its constituent terms for a set of numerical and semi-numerical simulations of a volume of (714 Mpc)³, focusing on large scales with k ≲ 0.3 Mpc⁻¹. We find that after ∼10 per cent of the universe has been ionized, the 21-cm power spectrum follows the power spectrum of neutral hydrogen fluctuations, which itself beyond a certain scale follows the matter power spectrum. Hence the signal has a two-regime form where the large-scale signal is a biased version of the cosmological density field, and the small-scale power spectrum is determined by the astrophysics of reionization. We construct a bias parameter to investigate the relation between the large-scale 21-cm signal and the cosmological density field. We find that the transition scale between the scale-independent and scale-dependent bias regimes is directly related to the value of the mean free path of ionizing photons (λ_MFP), and is characterised by the empirical formula k_trans ≈ 2/λ_MFP. Furthermore, we show that the numerical implementation of the mean free path effect has a significant impact on the shape of this transition. Most notably, the transition is more gradual if the mean free path effect is implemented as an absorption process rather than as a barrier.