The precise characterization and mitigation of systematic effects is one of the biggest roadblocks impeding the detection of the fluctuations of cosmological 21 cm signals. Missing data in radio cosmological experiments, often due to radio frequency interference (RFI), pose a particular challenge to power spectrum analysis as this could lead to the ringing of bright foreground modes in the Fourier space, heavily contaminating the cosmological signals. Here we show that the problem of missing data becomes even more arduous in the presence of systematic effects. Using a realistic numerical simulation, we demonstrate that partially flagged data combined with systematic effects can introduce significant foreground ringing. We show that such an effect can be mitigated through inpainting the missing data. We present a rigorous statistical framework that incorporates the process of inpainting missing data into a quadratic estimator of the 21 cm power spectrum. Under this framework, the uncertainties associated with our inpainting method and its impact on power spectrum statistics can be understood. These results are applied to the latest Phase II observations taken by the Hydrogen Epoch of Reionization Array, forming a crucial component in power spectrum analyses as we move toward detecting 21 cm signals in the ever more noisy RFI environment.

Detection of the faint 21 cm line emission from the Cosmic Dawn and Epoch of Reionisation will require not only exquisite control over instrumental calibration and systematics to achieve the necessary dynamic range of observations but also validation of analysis techniques to demonstrate their statistical properties and signal loss characteristics. A key ingredient in achieving this is the ability to perform high-fidelity simulations of the kinds of data that are produced by the large, many-element, radio interferometric arrays that have been purpose-built for these studies. The large scale of these arrays presents a computational challenge, as one must simulate a detailed sky and instrumental model across many hundreds of frequency channels, thousands of time samples, and tens of thousands of baselines for arrays with hundreds of antennas. In this paper, we present a fast matrix-based method for simulating radio interferometric measurements (visibilities) at the necessary scale. We achieve this through judicious use of primary beam interpolation, fast approximations for coordinate transforms, and a vectorised outer product to expand per-antenna quantities to per-baseline visibilities, coupled with standard parallelisation techniques. We validate the results of this method, implemented in the publicly-available matvis code, against a high-precision reference simulator, and explore its computational scaling on a variety of problems.

Deviations from Gaussianity in the distribution of the fields probed by large-scale structure surveys generate additional terms in the data covariance matrix, increasing the uncertainties in the measurement of the cosmological parameters. Super-sample covariance (SSC) is among the largest of these non-Gaussian contributions, with the potential to significantly degrade constraints on some of the parameters of the cosmological model under study -- especially for weak lensing cosmic shear. We compute and validate the impact of SSC on the forecast uncertainties on the cosmological parameters for the Euclid photometric survey, obtained with a Fisher matrix analysis, both considering the Gaussian covariance alone and adding the SSC term -- computed through the public code PySSC. The photometric probes are considered in isolation and combined in the `3$\times$2pt' analysis. We find the SSC impact to be non-negligible -- halving the Figure of Merit of the dark energy parameters ($w_0$, $w_a$) in the 3$\times$2pt case and substantially increasing the uncertainties on $\Omega_{{\rm m},0}, w_0$, and $\sigma_8$ for cosmic shear; photometric galaxy clustering, on the other hand, is less affected due to the lower probe response. The relative impact of SSC does not show significant changes under variations of the redshift binning scheme, while it is smaller for weak lensing when marginalising over the multiplicative shear bias nuisance parameters, which also leads to poorer constraints on the cosmological parameters. Finally, we explore how the use of prior information on the shear and galaxy bias changes the SSC impact. Improving shear bias priors does not have a significant impact, while galaxy bias must be calibrated to sub-percent level to increase the Figure of Merit by the large amount needed to achieve the value when SSC is not included.

ABSTRACT 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.

Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different time-scales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time. Applications of FR filtering include separating effects that are correlated with the rotating sky versus those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time, however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe-rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes-beam sidelobe/horizon suppression (the 'mainlobe' filter), and ground-locked systematics removal (the 'notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding.

The key to detecting neutral hydrogen during the epoch of reionization (EoR) is to separate the cosmological signal from the dominating foreground radiation. We developed direct optimal mapping (DOM) to map interferometric visibilities; it contains only linear operations, with full knowledge of point spread functions from visibilities to images. Here, we demonstrate a fast Fourier transform-based image power spectrum and its window functions computed from the DOM images. We use noiseless simulation, based on the Hydrogen Epoch of Reionization Array Phase I configuration, to study the image power spectrum properties. The window functions show <10(-11) of the integrated power leaks from the foreground-dominated region into the EoR window; the 2D and 1D power spectra also verify the separation between the foregrounds and the EoR.

This paper presents the design and deployment of the Hydrogen Epoch of Reionization Array (HERA) phase II system. HERA is designed as a staged experiment targeting 21 cm emission measurements of the Epoch of Reionization. First results from the phase I array are published as of early 2022, and deployment of the phase II system is nearing completion. We describe the design of the phase II system and discuss progress on commissioning and future upgrades. As HERA is a designated Square Kilometer Array (SKA) pathfinder instrument, we also show a number of "case studies" that investigate systematics seen while commissioning the phase II system, which may be of use in the design and operation of future arrays. Common pathologies are likely to manifest in similar ways across instruments, and many of these sources of contamination can be mitigated once the source is identified.

The small-scale CMB angular power spectrum contains many contaminants from secondary anisotropies created by large-scale structures. Although their contribution is taken into account in the analyses, their cosmological dependence is often ignored. We propose a new analysis of SPT data focusing on the cosmological contributions of the Sunyaev Zel’dovich effects (tSZ and kSZ). After modelling these two effects and building a power spectrum emulator, we show that using the cosmological information of the tSZ and kSZ in addition to that of the primordial CMB contained in the small-scale SPT data provides comparable constraints on the reionisation history to those of the large-scale data of Planck.

The cross-correlation between the 21 cm field and the galaxy distribution is a potential probe of the Epoch of Reionization (EoR). The 21 cm signal traces neutral gas in the intergalactic medium and, on large spatial scales, this should be anti-correlated with the high-redshift galaxy distribution which partly sources and tracks the ionized gas. In the near future, interferometers such as the Hydrogen Epoch of Reionization Array (HERA) are projected to provide extremely sensitive measurements of the 21 cm power spectrum. At the same time, the Nancy Grace Roman Space Telescope (Roman) will produce the most extensive catalog to date of bright galaxies from the EoR. Using semi-numeric simulations of reionization, we explore the prospects for measuring the cross-power spectrum between the 21 cm and galaxy fields during the EoR. We forecast a 14$\sigma$ detection between HERA and Roman, assuming an overlapping survey area of 500 deg$^2$, redshift uncertainties of $\sigma_z = 0.01$ (as expected for the high-latitude spectroscopic survey of Ly$\alpha$-emitting galaxies), and an effective Ly$\alpha$ emitter duty cycle of $f_\mathrm{LAE} = 0.1$. Thus the HERA-Roman cross-power spectrum may be used to help verify 21 cm detections from HERA. We find that the shot-noise in the galaxy distribution is a limiting factor for detection, and so supplemental observations using Roman should prioritize deeper observations, rather than covering a wider field of view.

The patchy kinetic Sunyaev-Zel'dovich (kSZ) signal is an integral probe of the timing and morphology of the epoch of reionization (EoR). Recent observations have claimed a low signal-to-noise (S/N) measurement, with a dramatic increase in S/N expected in the near future. In this work, we quantify what we can learn about the EoR from the kSZ signal. We perform Bayesian inference by sampling galaxy properties and using forward-models of the kSZ as well as other EoR and galaxy observations in the likelihood. Including the recent kSZ measurement obtained by the South Pole Telescope ($\mathcal{D}_{3000}^{\rm{pkSZ}} = 1.1_{-0.7}^{+1.1} \mu$K$^2$) shifts the posterior distribution in favor of faster and later reionization models, resulting in lower values of the optical depth to the CMB: $\tau_e = 0.052_{-0.008}^{+0.009}$ with a 68$\%$ confidence interval (C.I.). The combined EoR and UV luminosity function observations also imply a typical ionizing escape fraction of $0.04_{-0.03}^{+0.05}$ (95$\%$ C.I.), without a strong dependence on halo mass. We show how the patchy kSZ power from our posterior depends on the commonly-used parameters of reionization. For a given midpoint and duration, the EoR morphology only has a few percent impact on the patchy kSZ power in our posterior. However, a physical model is needed to obtain tight constraints from the current low S/N patchy kSZ measurement, as it allows us to take advantage of complimentary high-$z$ observations. Future high S/N detections of the patchy kSZ should decrease the current uncertainties on the timing of the EoR by factors of $\sim$2 - 3.

We report the most sensitive upper limits to date on the 21 cm epoch of reionization power spectrum using 94 nights of observing with Phase I of the Hydrogen Epoch of Reionization Array (HERA). Using similar analysis techniques as in previously reported limits, we find at 95% confidence that Δ 2 ( k = 0.34 h Mpc −1 ) ≤ 457 mK 2 at z = 7.9 and that Δ 2 ( k = 0.36 h Mpc −1 ) ≤ 3496 mK 2 at z = 10.4, an improvement by a factor of 2.1 and 2.6, respectively. These limits are mostly consistent with thermal noise over a wide range of k after our data quality cuts, despite performing a relatively conservative analysis designed to minimize signal loss. Our results are validated with both statistical tests on the data and end-to-end pipeline simulations. We also report updated constraints on the astrophysics of reionization and the cosmic dawn. Using multiple independent modeling and inference techniques previously employed by HERA Collaboration, we find that the intergalactic medium must have been heated above the adiabatic cooling limit at least as early as z = 10.4, ruling out a broad set of so-called “cold reionization” scenarios. If this heating is due to high-mass X-ray binaries during the cosmic dawn, as is generally believed, our result’s 99% credible interval excludes the local relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars.

Combining the visibilities measured by an interferometer to form a cosmological power spectrum is a complicated process. In a delay-based analysis, the mapping between instrumental and cosmological space is not a one-to-one relation. Instead, neighbouring modes contribute to the power measured at one point, with their respective contributions encoded in the window functions. To better understand the power measured by an interferometer, we assess the impact of instrument characteristics and analysis choices on these window functions. Focusing on the Hydrogen Epoch of Reionization Array (HERA) as a case study, we find that long-baseline observations correspond to enhanced low-k tails of the window functions, which facilitate foreground leakage, whilst an informed choice of bandwidth and frequency taper can reduce said tails. With simple test cases and realistic simulations, we show that, apart from tracing mode mixing, the window functions help accurately reconstruct the power spectrum estimator of simulated visibilities. The window functions depend strongly on the beam chromaticity, and less on its spatial structure - a Gaussian approximation, ignoring side lobes, is sufficient. Finally, we investigate the potential of asymmetric window functions, down-weighting the contribution of low-k power to avoid foreground leakage. The window functions presented here correspond to the latest HERA upper limits for the full Phase I data. They allow an accurate reconstruction of the power spectrum measured by the instrument and will be used in future analyses to confront theoretical models and data directly in cylindrical space.

Super-sample covariance (SSC) is an important effect for cosmological analyses that use the deep structure of the cosmic web; it may, however, be nontrivial to include it practically in a pipeline. We solve this difficulty by presenting a formula for the precision (inverse covariance) matrix and show applications to update likelihood or Fisher forecast pipelines. The formula has several advantages in terms of speed, reliability, stability, and ease of implementation. We present an analytical application to show the formal equivalence between three approaches to SSC: (i) at the usual covariance level, (ii) at the likelihood level, and (iii) with a quadratic estimator. We then present an application of this computationally efficient framework for studying the impact of inaccurate modelling of SSC responses for cosmological constraints from stage IV surveys. We find that a weak-lensing-only analysis is very sensitive to inaccurate modelling of the scale dependence of the response, which needs to be calibrated at the ∼15% level. The sensitivity to this scale dependence is less severe for the joint weak-lensing and galaxy clustering analysis (also known as 3×2pt). Nevertheless, we find that both the amplitude and scale-dependence of the responses have to be calibrated at better than 30%.

Recent measurements from the CMB and from high-redshift galaxy observations have placed rough constraints on the midpoint and duration of the Epoch of Reionization. Detailed measurements of the ionization history remain elusive, although two proposed probes show great promise for this purpose: the 21cm global signal and the kinetic Sunyaev-Zel’dovich (kSZ) effect. We formally confirm the common assumption that these two probes are highly complementary, with the kSZ being more sensitive to extended ionization histories and the global signal to rapidly evolving ones. We do so by performing a Karhunen-Loève (KL) transformation, which casts the data in a basis designed to emphasize the information content of each probe. We find that reconstructing the ionization history using both probes gives significantly more precise results than individual constraints, although carefully chosen, physically motivated priors play a crucial part in obtaining a bias-free reconstruction. Additionally, in the KL basis, measurements from one probe can be used to detect the presence of residual systematics in the other, providing a safeguard against systematics that would go undetected when data from each probe is analyzed in isolation. Once detected, the modes contaminated by systematics can be discarded from the data analysis to avoid biases in reconstruction.

Small scale CMB angular power spectrum contains not only primordial CMB information but also many contaminants coming from secondary anisotropies. Most of the latter depend on the cosmological model but are often marginalised over. We propose a new analysis of the SPT data focusing on the cosmological contribution of the thermal Sunyaev Zel'dovich (tSZ) effect. We model the tSZ angular spectrum with the halo model and train a random forest algorithm to speed up its computation. We show that using the cosmological information of the tSZ on top of the primordial CMB one contained in SPT data bring more constraints on cosmological parameters. We also combine for the first time Planck tSZ angular power spectrum with SPT ones to put further constraints. This proof of concept study shows how much a proper modelling of the foregrounds in the cosmological analyses is needed.

Recent results of ground-based telescopes, giving high-quality measurements of the CMB temperature power spectrum on small scales motivate the need for an accurate model of foregrounds, which dominate the primary signal at these multipoles. In a previous work, we have shown that cosmological information could be retrieved from the power spectrum of the thermal SZ effect. In this work, we introduce a physically motivated model of the Epoch of Reionisation in the cosmological analysis of CMB data, which is coherent on all scales. In particular, at high multipoles, the power spectrum of the kinetic SZ (kSZ) effect is inferred from a set of cosmological and reionisation parameters by a machine-learning algorithm. First including an asymmetric parameterisation of the reionisation history in the Planck 2018 data analysis, we retrieve a value of the optical depth consistent with previous results, but stemming from a completely different history of reionisation in which the first luminous sources light up as early as $z=15$. Considering the latest small-scale data from the SPT and letting the cosmology free to vary, we find that including the new cosmology-dependent SZ spectra helps tighten the constraints on their amplitudes by breaking their degeneracy. We report a $5\sigma$ measurement of the kSZ signal at $\ell=3000$, $\mathcal{D}_{3000}^\mathrm{kSZ} = 3.4^{+0.5}_{-0.3}\,\mu\mathrm{K}^2$ at the 68% confidence level, marginalised over cosmology, as well as an upper limit on the patchy signal from reionisation $\mathcal{D}_{3000}^\mathrm{pkSZ}<1.6~\mu\mathrm{K}^2$ (95% C.L.). Additionally, we find that the SPT data favour slightly earlier reionisation scenarios than Planck, leading to $\tau = 0.062 ^{+0.012}_{-0.015}$ and a reionisation midpoint $z_\mathrm{re} = 7.9^{+1.1}_{-1.3}$ (68% C.L.), which is in line with constraints from high-redshift quasars and galaxies.

We propose a new analysis of small scale CMB data by introducing the cosmological dependency of the foreground signals, focusing first on the thermal Sunyaev-Zel'dovich (tSZ) power spectrum, derived from the halo model. We analyse the latest observations by the South Pole Telescope (SPT) of the high-$\ell$ power (cross) spectra at 90, 150 and 220 GHz, as the sum of CMB and tSZ signals, both depending on cosmological parameters, and remaining contaminants. In order to perform faster analyses, we propose a new tSZ modelling based on machine learning algorithms (namely Random Forest). We show that the additional information contained in the tSZ power spectrum tightens constraints on cosmological and tSZ scaling relation parameters. We combine for the first time the Planck tSZ data with SPT high-$\ell$ to derive even stronger constraints. Finally, we show how the amplitude of the remaining kSZ power spectrum varies depending on the assumptions made on both tSZ and cosmological parameters.

Photometric galaxy surveys probe the late-time Universe where the density field is highly non-Gaussian. A consequence is the emergence of the super-sample covariance (SSC), a non-Gaussian covariance term that is sensitive to fluctuations on scales larger than the survey window. In this work, we study the impact of the survey geometry on the SSC and, subsequently, on cosmological parameter inference. We devise a fast SSC approximation that accounts for the survey geometry and compare its performance to the common approximation of rescaling the results by the fraction of the sky covered by the survey, $f_\mathrm{SKY}$, dubbed 'full-sky approximation'. To gauge the impact of our new SSC recipe, dubbed 'partial-sky', we perform Fisher forecasts on the parameters of the $(w_0,w_a)$-CDM model in a 3x2 points analysis, varying the survey area, the geometry of the mask and the galaxy distribution inside our redshift bins. The differences in the marginalised forecast errors, with the full-sky approximation performing poorly for small survey areas but excellently for stage-IV-like areas, are found to be absorbed by the marginalisation on galaxy bias nuisance parameters. For large survey areas, the unmarginalised errors are underestimated by about 10% for all probes considered. This is a hint that, even for stage-IV-like surveys, the partial-sky method introduced in this work will be necessary if tight priors are applied on these nuisance parameters.

Combining the visibilities measured by an interferometer to form a cosmological power spectrum is a complicated process in which the window functions play a crucial role. Indeed, in a delay-based analysis, the mapping between instrumental space, made of per-baseline delay spectra, and cosmological space is not a one-to-one relation. Instead, neighbouring modes contribute to the power measured at one point, with their respective contributions encoded in the window functions. To better understand the power measured by an interferometer, we assess in this paper the impact of instrument characteristics and analysis choices on the power spectrum estimator by deriving its exact window functions outside of the delay approximation. Focusing on the Hydrogen Epoch of Reionization Array (HERA) as a case study, we find that observations made with long baselines tend to correspond to enhanced low- 𝑘 tails of the window functions, which facilitate foreground leakage outside the wedge, whilst the choice of bandwidth and frequency taper can help narrowing them down. With the help of simple test cases and more realistic visibility simulations, we show that, apart from tracing mode mixing, the window functions can accurately reconstruct the power spectrum estimator of simulated visibilities. We note that the window functions depend strongly on the chromaticity of the beam, and less on its spatial structure – a Gaussian approximation, ignoring side lobes, is sufficient. Finally, we investigate the potential of asymmetric window functions, down-weighting the contribution of low- 𝑘 power to avoid foreground leakage. The window functions presented in this work correspond to the latest HERA upper limits for the full Phase I data. They allow an accurate reconstruction of the power spectrum measured by the instrument and can be used in future analyses to confront theoretical models and data directly in cylindrical space.

Intensity mapping of the 21cm signal of neutral hydrogen will yield exciting insights into the Epoch of Reionisation and the nature of the first galaxies. However, the large amount of data that will be generated by the next generation of radio telescopes, such as the Square Kilometre Array (SKA), as well as the numerous observational obstacles to overcome, require analysis techniques tuned to extract the reionisation history and morphology. In this context, we introduce a one-point statistic, to which we refer as the local variance, $\sigma_\mathrm{loc}$, that describes the distribution of the mean differential 21cm brightness temperatures measured in two-dimensional maps along the frequency direction of a light-cone. The local variance takes advantage of what is usually considered an observational bias, the sample variance. We find the redshift-evolution of the local variance to not only probe the reionisation history of the observed patches of the sky, but also trace the ionisation morphology. This estimator provides a promising tool to constrain the midpoint of reionisation as well as gaining insight into the ionising properties of early galaxies.