We present meer21cm, a comprehensive python package for cosmological data analysis of single-dish HI intensity mapping surveys. This package is simple to use, with a modularised code structure designed for interactive usage. meer21cm is designed for data analysis, with particular focus on the UHF-band observation of MeerKAT Large Area Synoptic Survey (MeerKLASS). We explicitly impose meer21cm to be survey-oriented, ensuring consistent modelling of observational effects in the clustering power spectrum with the survey specifications and data analysis choices. meer21cm covers a large range of data analysis procedures post calibration, including data read-in, foreground cleaning, power spectrum estimation, mock simulation, transfer function corrections and parameter inference. It handles both meer21cm intensity maps and overlapping galaxy catalogues, allowing for multi-tracer and cross-correlation analysis between MeerKLASS and optical galaxy surveys. Tested with a simulated survey of ten 750deg^2 sky patches in the redshift sub-band 0.6 < z < 0.8, the meer21cm pipeline achieves per-cent accuracy in the power spectrum estimation for k ∈ [0.02, 0.2] h Mpc^-1, with deviations ≲ 0.5σ between the mock and the model power spectra, where σ is the signal variance. The meer21cm package is publicly available and easy to install, with a comprehensive documentation website at https://meer21cm.readthedocs.io

Advancing Astrophysics with the SKA II (AASKAII), written by our science community, outlines the transformative scientific advances that will be enabled by the SKA telescopes. In the decade since the publication of the previous edition, telescope designs have matured, construction has commenced, and the SKA Organisation has evolved into the SKA Observatory (SKAO). At the same time, observations from SKA precursor and pathfinder telescopes have provided new insights into longstanding scientific challenges while revealing entirely new phenomena. Published in advance of the first science verification campaign for the SKA Observatory, this volume looks ahead to the coming decades of discovery and innovation in radio astronomy. AASKAII spans the broad range of scientific research enabled by the SKA telescopes, SKA-Mid and SKA-Low. The contributions are organised into six thematic categories according to their scientific focus. The opening section presents overview chapters from the SKA Science Working Groups, around which our community is organised. Each overview provides the broader context that connects the contributions in this volume to the key scientific questions being pursued by their respective communities.

On the scale of the cosmic horizon, signatures that are unique to general relativity are concealed within the statistics of the large scale distribution of galaxies. These were thought to be beyond the reach of all but the most ambitious galaxy surveys, as they are substantially suppressed relative to standard redshift-space distortions. We show that the detectability of these higher-order relativistic effects can be dramatically enhanced by a sampling strategy that splits a galaxy catalogue into faint and bright subsamples and then combines their auto-bispectra. For current surveys such as DESI, this implies that this new signal will be detectable for the first time using our new strategy.

Context. H I intensity mapping is a promising technique to probe large-scale structure, traditionally analyzed via two-point statistics such as the angular power spectrum. This latter technique has proven very powerful but may miss key non-Gaussian information present in the signal. Aims. We extend the starlet ℓ1-norm, a multi-scale higher-order statistic previously applied to weak lensing maps, to the brightness temperature fluctuations of the H I density field. The H I signal is highly non-Gaussian at late times (z < 1) due to nonlinear structure growth, motivating the use of advanced summary statistics. Methods. We simulated full-sky H I lognormal brightness temperature maps using CAMB and GLASS, generating 10 000 realizations with associated cosmological parameters. We extracted both the starlet ℓ1-norm and angular power spectrum from these maps. Using the JaxILI framework, we performed neural density estimation for implicit likelihood inference. The analysis considered simulated maps incorporating realistic noise and telescope beam, capturing the impact of observational effects on parameter inference. In this work, we focus on the redshift range 0.4 < z < 0.45, chosen to match the interval already targeted by existing MeerKLASS observations. We also assess the sensitivity of these statistics to observational systematics, highlighting their potential for identifying and mitigating contaminants in H I intensity maps. Results. The starlet ℓ1-norm significantly outperforms the angular power spectrum in constraining cosmological parameters, achieving almost a 3× improvement in the figure of merit relative to the angular power spectrum by capturing non-Gaussian features missed by two-point statistics. Moreover, our results suggest that the starlet ℓ1-norm is robust to several of the systematic effects included in our simulations. Conclusions. Our findings highlight the potential of multi-scale higher-order statistics such as the starlet ℓ1-norm to enhance cosmological inference from future H I intensity mapping surveys.

The SKA telescopes will revolutionise our ability to do cosmology at radio wavelengths, via both their own data and in synergy with other wavelengths. SKAO will be the first instrument able to conduct large-scale cosmological surveys as done in the last decades in the optical and near-infrared. This complementarity will be vital as cosmology hits the limit of systematic uncertainties. Radio cosmology surveys will have radically different systematics, allowing data combinations across surveys to calibrate systematics and increase overall constraining power. Neutral hydrogen (HI) intensity mapping surveys are now reaching maturity, as demonstrated by the progress made by the MeerKLASS survey with MeerKAT. Along with continuum galaxy surveys, they will provide detailed maps of the Universe covering large fractions of the sky, allowing us to answer questions about fundamental physics which can only be measured on the largest scales. In combination with weak lensing and HI galaxy probes, HI intensity maps will also measure the distributions of matter and velocities to give precisions tests of the ΛCDM model, including its foundational assumptions of isotropy and homogeneity. In combination with gravitational wave observations and fast radio bursts, they will also help us measure the expansion history and baryon content of the Universe. Here we provide an overview of the achievements of precursor surveys and the progress towards SKA cosmology, starting with AA* and reaching full maturity with AA4 telescopes.

Our understanding of the 7-ray sky has greatly advanced, yet studying the unresolved 7-ray background (UGRB) can unveil the nature of the faintest 7-ray source populations in the Universe. Statistical cross-correlations between the UGRB and tracers of large-scale cosmic structure allow us to infer which sources contribute the most to this emission. In this work, we examine the angular correlation between the UGRB and the matter distribution traced by galaxies, using twelve years of Fermi Large Area Telescope (LAT) observations along with three years of Dark Energy Survey (DES) data. We detect a correlation with a signal-to-noise ratio of 7.85, primarily driven by large angular scales. We then perform a multi-tracer analysis that combines this measurement with the cross-correlation between 7 rays and DES weak lensing. The two single-tracer results are mutually consistent, and their combination yields a total significance of 10.31, firmly establishing the extragalactic origin of the UGRB. Intriguingly, the properties inferred for the sources contributing to the UGRB show departures from those of the resolved 7-ray population, suggesting that the faint end of the 7-ray sky is not a simple extrapolation of currently resolved sources.

Using the SKAO to map the intensity of neutral hydrogen's 21cm emission line will be a golden opportunity to constrain models of cosmology. To access the largest cosmological scales, wide-sky surveys should ideally reach thousands of square degrees, requiring SKA-Mid's dishes to scan the sky in auto-correlation mode, so-called single-dish observations. In this chapter, we overview the latest results from MeerKAT's Large Area Synoptic Survey (MeerKLASS), which has been pioneering this single-dish observing strategy, and motivating its continuation with the SKA-Mid AA4 deployment. MeerKLASS, operating on the same Karoo site where the SKA-Mid is being built, has now achieved multiple cosmological detections from single-dish observations, including high-significance cross-correlations with optical galaxy surveys and continually improving measurements of the HI auto-power spectrum. These results demonstrate that stable calibration, effective foreground mitigation, and statistical recovery of cosmological signal are all achievable with a large multi-dish telescope in total-power mode. The success of MeerKLASS therefore validates the observational strategies required for SKA-Mid and marks a key milestone in demonstrating the viability of single-dish HI intensity mapping for cosmology. Looking ahead, SKA-Mid's increased sensitivity and Band 1 coverage (350-1050 MHz) will allow the same methodology to probe redshifts up to z ∼ 3, mapping volumes several orders of magnitude larger than currently accessible. The techniques refined with MeerKLASS thus form the operational and scientific foundation for a large portion of the SKAO's cosmology programme.

The origins of the universe remain one of the biggest mysteries in modern cosmology. While the Planck satellite has provided a wealth of information about the early universe, there is still much to be discovered. The Square Kilometre Array Observatory (SKAO) offers a unique opportunity to probe the universe's infancy, going beyond the current limitations of our knowledge. By measuring the power spectrum of biased tracers of the dark matter distribution on the largest cosmological scales and exploring beyond 2-point statistics, SKAO will enable us to refine our understanding of the primordial universe, including the shape of the inflationary power spectrum and the presence of primordial non-Gaussianity. In this chapter we will review recent works looking at the potential of SKAO's surveys, and how synergies with other surveys can revolutionize our understanding of the origins of the cosmos.

A major goal of ongoing and future cosmological surveys of the large-scale structure is to measure local type primordial non-Gaussianity in the galaxy power spectrum through the scale-dependent bias. General relativistic effects have been shown to be degenerate with this measurement and therefore one needs to consider a non-Newtonian approach. In this work, we develop a consistent framework to compute integrated effects, including lensing convergence, time delay, and integrated Sachs-Wolfe, along with the local relativistic projection and wide-separation corrections in the multipoles of the power spectrum. We show that, for a Euclid-like H alpha-line galaxy survey and a MegaMapper-like Lyman-break galaxy survey, ignoring these effects leads to a bias on the best fit measurement of the amplitude of primordial non-Gaussianity, fNL, of around 3 sigma and 20 sigma respectively. When we include these corrections, the uncertainty in our knowledge of the luminosity function leads to further uncertainty in our measurement of fNL. However, we show that this degeneracy can be partly mitigated by using a bright-faint multi-tracer analysis, where the observed galaxy sample is subdivided into two separate populations based on luminosity. This provides a 15-20% improvement on the forecasted constraints of local type fNL. In addition, we present a novel calculation of the full multi-tracer covariance with the inclusion of wide-separation corrections. All of these results are implemented in the Python code COSMOWAP.

We present a science case to perform high-redshift cosmic shear surveys for cosmology with next-generation spectroscopic instruments, such as the proposed MegaMapper and Wide-field Spectroscopic Telescope. We argue that by using the novel technique called 'kinematic lensing' (KL) it will be possible to obtain shear catalogues at redshifts between 2 and 5. We show that the signal-to-noise ratio of KL at such high redshifts is on average twice as much that expected from current weak lensing (WL) surveys such as Euclid or LSST, and several times that of the previous generation of WL surveys like DES and KiDS, even with very conservative assumptions about the fraction of spectroscopically-detected sources for which KL shear estimates will be available. This will allow cosmologists to perform joint galaxy clustering-cosmic shear analyses over unprecedented cosmic volumes and to probe the growth of structures deep in the matter-dominated era and across the onset of dark-energy domination, offering a unique opportunity to unveil the mystery of cosmic acceleration.

Mapping the integrated 21 cm emission line from dark matter-tracing neutral hydrogen gas is the primary science goal for MeerKLASS (MeerKAT’s Large Area Synoptic Survey). Prior to the arrival of MeerKAT, this intensity mapping technique had only been tested on a couple of pre-existing single-dish radio telescopes with a handful of observational hours with which to make early pioneering detections. The 64-dish MeerKAT array, precursor to the SKA Observatory (SKAO), can scan the sky in auto-correlation (or single-dish) mode and perform intensity mapping across large sky areas, presenting the exciting potential for a wide area ( ≳ 10,000 deg^2 ) spectroscopic survey across redshift 0.4 < z < 1.45 . Validating the single-dish mode of observation for a multi-dish array and developing the analysis pipeline with which to make unbiased measurements has presented major challenges to this endeavour. In this work, we overview the advances in the field that have facilitated a robust analysis framework for single-dish intensity mapping, and review some results that showcase its success using early MeerKLASS surveys. We demonstrate our control of foreground cleaning, signal loss and map regridding to deliver detections of cosmological clustering within the intensity maps through cross-correlation power spectrum measurements with overlapping galaxy surveys. Finally, we discuss the prospects for future MeerKLASS observations and forecast its potential, making our code publicly available: .

The SKA Observatory will enable measurements of the Tully-Fisher relation for statistical samples of HI selected galaxies out to unprecedented depths and redshifts thanks to its unique combined spatial and spectral sensitivity. This chapter explores the transformative potential of such surveys for cosmology, in particular in the field of peculiar velocity measurements. We briefly review the present observational landscape for Tully-Fisher HI galaxy surveys and existing peculiar velocity datasets, and compare them with predictions for SKAO Tully-Fisher HI galaxy surveys with AA* and AA4 configurations of the SKA-Mid array. We discuss the extended range of cosmology science cases covered and enabled by such surveys.

We present a comparative overview of state-of-the-art methods for modelling the distribution of neutral hydrogen (HI) in the post-reionization Universe, developed in preparation for upcoming SKAO cosmological surveys. Our aim is to assess how different physical and empirical assumptions reflect into predictions for key observables such as the cosmic HI density, the HI mass function, and the HI-halo mass relation. We consider both: (i) semi-analytical approaches that self-consistently evolve baryonic components within dark matter merger trees through physically motivated prescriptions and (ii) empirical schemes tailored to different observables and based on fast approximations designed for large ensemble studies. By comparing the predictions from the different methods considered, we find overall consistency in integrated quantities such as Ω_HI, yet systematic differences in the detailed shape and scatter of the HI–halo mass relation and its redshift evolution. Semi-analytical models offer physically grounded predictions but depend on assumed prescriptions, while empirical methods provide flexibility and computational efficiency at the expense of robustness in extrapolated regions of the parameter space. The increasing number of HI measurements from SKA precursors and pathfinders (including surveys with MeerKAT, ASKAP, and FAST) will provide critical observational constraints to refine and calibrate current simulation methodologies. In turn, increasingly realistic HI simulations play a key role in interpreting these data, guiding survey design and analysis strategies, in preparation for the advent of SKAO data.

Accurate modelling of the covariance of clustering observables is essential to fully exploit current and future survey data, which is expected to constrain large-scale clustering signals with unprecedented precision. Computational costs of simulation-based estimates motivate analytical approaches, especially in light of the growing interest towards multi-tracer analyses and parity-odd signatures in two-point statistics, which respectively mitigate cosmic variance and probe relativistic projection effects on cosmological scales. In this work, we generalise previous theoretical results for the Gaussian covariance of multi-tracer power spectrum measurements, providing a general expression applicable to both real (even-parity) and complex (both even- and odd-parity) power spectra. We focus on a generic weighted estimator at first, and then showcase how our general formalism applies to Legendre power spectrum multipoles and two-dimensional power spectrum, recovering known limits in appropriate cases. We validate our predictions against Gaussian Monte Carlo simulations and investigate the structure of the covariance matrix, including the Hermitian properties of its imaginary part.

The cosmological distribution of neutral hydrogen (HI) during the post-reionization era is highly non-Gaussian due to the underlying non-linear structure formation, complex galaxy biasing, and potential primordial non-Gaussianity. One needs higher-order (beyond two-point) statistics to maximally extract the non-Gaussian information out of the 21-cm intensity maps. This chapter summarizes the potential of several higher-order statistics, including voxel intensity distribution, emission line stacking, probability density functions, ℓ_1-norm, bispectrum, and various marked statistics. Additionally, image-based morphological descriptors, such as the Largest Cluster Statistic, local dimensions, and Minkowski functionals, etc., can potentially characterize the morphology and geometry of the cosmic web encoded in the 21-cm intensity maps. This chapter presents forecasts of the detectability of these higher-order statistics in the context of the future SKAO observations. These forecasts incorporate instrumental noise, observational effects, and, in some cases, foreground removal in their analyses. With its unprecedented sensitivity, the future SKAO 21-cm observations will enable us to measure these higher-order statistics more precisely, possibly helping to break degeneracies between astrophysical and cosmological parameters, and maximizing the science outcome from these surveys.

The distribution of neutral hydrogen (HI) in the post-reionization universe traces the cosmic large-scale structure and therefore serves as a powerful cosmological probe. An efficient way to measure its distribution over wide sky areas and redshift ranges is through single-dish intensity mapping, which exploits the autocorrelation signal of each dish in a telescope array while scanning the same sky patch. Thanks to its broad frequency coverage and technical capabilities, SKA-Mid will enable measurements of the integrated 21 cm emission from HI up to redshift z∼3, making single-dish intensity mapping a key observable for probing dark matter and dark energy. Isolating the faint 21 cm cosmological signal without introducing biases is, however, challenging. The 21 cm signal is several orders of magnitude weaker than the astrophysical foregrounds, and its analysis is further affected by instrumental systematics. Overcoming these difficulties requires detailed modelling together with continuous improvements and innovations in data-analysis techniques. Over the past decade, the international community has developed and tested new methods to address current observational challenges and prepare for forthcoming SKA-Mid observations. This chapter reviews recent advances in map-making and component-separation techniques, with particular emphasis on telescope-specific systematics such as beam response and correlated noise. We focus on results obtained in controlled simulation environments, providing a valuable framework for assessing the strengths and limitations of different approaches. Developing robust algorithms capable of accurately handling instrumental effects and sky-model uncertainties is a crucial step toward fully exploiting the cosmological potential of HI intensity-mapping surveys in the SKA Observatory era.

General relativity is exquisitely tested in strong-field regimes, yet its validity on cosmological scales remains largely unexplored. Upcoming wide and deep large-scale structure surveys will access the ultra-large, linear scales where relativistic effects - Doppler terms, gravitational redshift, lensing magnification, and potential evolution - leave significant imprints in the clustering of galaxies. These signatures represent unique probes of spacetime that are inaccessible to standard Newtonian analyses but increasingly important as survey volumes grow. We outline the scientific potential of next-generation facilities, such as those envisioned within ESO's Expanding Horizons programme, to deliver the first robust measurements of relativistic effects in large-scale structure through multi-tracer power spectra and the single-tracer bispectrum of high-redshift Lyman-break galaxies. Detecting these contributions would open a new window on gravity, enabling precision tests of general relativity and its alternatives on cosmological scales in the 2040s.

The 21-cm line from neutral hydrogen has long been recognised as a promising tracer of the large-scale structure of the Universe. The line is weak however, making individual galaxy detections quite inefficient, especially at higher redshifts. The technique of 21-cm intensity mapping has been pioneered over the last two decades to address this limitation. Instead of detecting individual galaxies, the brightness temperature field from the combined 21-cm emission of many unresolved galaxies is mapped as a function of angle and frequency, resulting in 3D tracer maps of the large-scale structure. In this chapter, we review the major pioneering efforts to develop this observable into a competitive cosmological tool, paying particular attention to the status of pathfinder observations that have paved the way for a large and highly sensitive 21-cm intensity mapping survey with the SKA-Mid telescope.

The redshifted spectral emission from neutral hydrogen (HI) at rest wavelength 21 cm can be used as a tracer of large-scale structure and its evolution. Within the HI intensity mapping method, sufficient signal-to-noise is achieved by integrating the line emission within large voxels over a wide sky area and line of sight depth which allows access to the largest scales of the matter distribution. The resulting tomographic maps usually feature low angular and high redshift resolution. The SKAO will be able to conduct HI intensity mapping experiments observing up to 20,000 square degrees over a wide range of redshifts. For SKA-Mid, we will employ the array in a fast-scanning single-dish mode using Band 1 and 2 to access 0<z<3, mapping an enormous volume with fast survey speed, allowing for the possibility of a commensal survey producing high angular resolution maps via the on-the-fly imaging of the visibilities. For SKA-Low, we will focus on deep observations to detect the HI signal in a frequency band matching 3<z<6. In this chapter, we will give an overview of HI intensity mapping with the SKAO, including an outline of planned surveys, a discussion of observational challenges, and methodology for power spectrum methodology and forecasts. We present predictions on the constraining power on LambdaCDM cosmology from HI intensity mapping data via power spectrum, and other observables such as bi-spectrum and HI stacking. We also demonstrate the synergy power of HI intensity mapping with other cosmological surveys.

We discuss the power of weak gravitational lensing surveys with the SKAO in constraining cosmological parameters and the properties of radio star-forming galaxy samples. As well as reviewing progress to date on cosmic shear in radio experiments, we show forecasts for parameter constraints using the Mid telescope both alone and in cross-correlation with contemporaneous optical surveys. By selecting a sample of resolved, high-redshift star-forming galaxies in Band 2, surveys with the AA4 configuration will be capable of measuring the growth of structure on large scales in the Universe through the effect of weak gravitational lensing on their shapes. Assuming the high fidelity reconstruction of such galaxy shapes to be possible, we find that SKAO will measure the S_8 structure formation parameter to a level of 5% alone and 3% in full combination with either LSST or the Euclid satellite. These measurements will be highly important due to their radically different sensitivities to key weak lensing systematics, both instrumental and astrophysical, and as such provide a vital robustness test to a pillar of modern cosmological measurements. Radio surveys also provide unique and potentially game-changing information in the form of polarisation and galaxy kinematics, which allow the cleaner separation of lensing from intrinsic galaxy shapes and can increase statistical power by factors ∼5-10.