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Morphological summary statistics, such as Minkowski functionals, Betti numbers and Minkowski tensors, provide a route to carry out cosmological data analysis which is complementary to traditional mode decomposition based statistics such as the power spectrum. We summarize the properties of these statistics and demonstrate their information content by using the gravitational evolution of matter and 21-cm brightness temperature as physical examples.

The formation of the first stars in the Universe remains a key challenge in cosmology, requiring a multi-wavelength observational strategy across a range of facilities. Telescopes like the James Webb Space Telescope (JWST) enable direct observation of early galaxies, while upcoming radio telescopes such as the SKA will capture the hydrogen signal from the early Universe. Interpreting the extensive datasets from these facilities demands sophisticated theoretical models that balance detailed physics with computational efficiency, supported by advanced statistical methods to probe the parameter space. In this talk, we will discuss recent advancements in modelling the high-redshift Universe, along with the evolution of machine learning-driven statistical techniques. Together, these developments are essential for bridging the gap between theoretical predictions and observations, enabling a deeper understanding of cosmic evolution with next-generation observational capabilities.

In this talk I will describe recent work done by the MIST Global 21-cm experiment. The focus will be on sky observations conducted from the Canadian High Arctic and on efforts to calibrate these observations with high accuracy.

During the Epoch of Reionisation (EoR), the ultraviolet radiation from the first stars and galaxies ionised the neutral hydrogen of the intergalactic medium, which itself can emit radiation through the 21 cm hyperfine transition. Due to this, the 21 cm signal is a direct probe of the first stars in the early Universe and a key science goal for the future Square Kilometre Array (SKA). However, observing and interpreting this signal is a notoriously difficult task.

Another high-potential probe is the patchy kinetic Sunyaev-Zel'dovich effect (pkSZ). Induced by the scattering of Cosmic Microwave Background (CMB) photons with a medium of free electrons produced during the EoR, the effect altered the small-scale CMB temperature anisotropies, imprinting information on the growth of ionising bubbles from the first galaxies. While measurements of the pkSZ angular power spectrum by Reichardt et al. (2021) have reported a 3σ constraint of D^pkSZ (l=3000) = 3.0 ± 1.0 μK2, the results are also subject to modelling uncertainties.

In this talk, we propose a simple yet effective parametric model that establishes a formal connection between the 21 cm and pkSZ power spectra. Using this model to jointly fit mock 21 cm and pkSZ data points, we confirm that these two observables exhibit complementary characteristics, leading to significantly improved constraints on reionisation compared to analysing each data set separately. Our findings demonstrate that a few well-informed low-redshift (eg., z < 8) measurements of the 21 cm power spectrum at k ≈ 0.1 cMpc^-1 and pkSZ power spectra can precisely determine the reionisation history of the Universe.

Therefore, even in the early stages of observations with the SKA, we can begin to constrain cosmic reionisation by performing a combined analysis of the 21 cm power spectrum with the pkSZ observations.

The observations of the redshifted 21-cm signal contain a wealth of cosmological and astrophysical information. The study of this signal from the high redshift Universe provides a unique opportunity to learn about the properties of the first stars and galaxies. However, the problem is particularly challenging due to the presence of foregrounds and system noise. In this talk, I will talk about different statistical estimators to measure the cosmological 21-cm signal from radio interferometric observations. Also, I will present our recent results towards detecting this faint 21-cm signal using the uGMRT and the MWA low-frequency observations.

The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a drift-scan radio interferometer located at the Dominion Radio Astrophysical Observatory (DRAO) in Penticton, British Columbia, Canada. CHIME, operating between 400 and 800 MHz, will map the redshifted 21 cm emission of neutral hydrogen between redshifts z = 0.8 − 2.5 across the northern sky. The 21cm line is a tracer of the large-scale structure of matter, whose statistics encode a well-understood standard ruler, the baryon acoustic oscillation scale. By detecting and tracking the evolution of this scale with redshift, CHIME aims to constrain the expansion history of the Universe over this crucial redshift epoch when the overall energy density of the Universe is expected to have become dominated by dark energy.

However, measuring this cosmological signal is challenging due to bright astrophysical foregrounds, which are about 4-5 orders of magnitude brighter than the cosmological HI signal.

In principle, these two signals can be separated due to their different spectral features, in which, the foreground signal is smooth in frequency, whereas the cosmological signal has spectral structure. However, this separation requires an instrument calibration at the sub-percent level accuracy. Recently, the CHIME collaboration reported the detection of cosmological 21 cm emission from a large-scale structure between redshift 0.78 and 1.43 in cross-correlation with eBOSS galaxy and quasar catalogs. In this cross-correlation measurement, a high-pass filter is applied to the frequency axis of each map pixel to remove foregrounds, which results in a measurement of the cosmological signal at the non-linear scales. I will discuss recent results in measuring the 21 cm signal in auto-correlation and some of the challenges that we have encountered. I will describe the improvements in the data processing and various data quality cuts required to measure the signal in auto-correlation. I will show the first results of the power spectrum using CHIME data.

The study of the Universe's large-scale structure and evolution has entered a new era with the emergence of neutral hydrogen intensity mapping as a powerful observational technique. HI intensity mapping (IM) offers a unique and innovative approach to cosmological research by probing the distribution of neutral hydrogen on vast scales. This technique uses radio telescopes like MeerKAT to detect the cumulative 21cm emission from neutral hydrogen. In this talk, I will introduce our current HI IM experiment with MeerKAT in the post-reionization universe and discuss our recent breakthroughs in the field. Additionally, I will present the on-the-fly (OTF) interferometric imaging capabilities with MeerKAT. Our aim is to explore cosmology through single-dish HI intensity mapping while simultaneously generating continuum images via the interferometer. This technique allows for commensal observing for both intensity mapping and interferometric imaging. We plan to survey an extensive 10,000 square degrees in the UHF band, achieving a sensitivity of 25 uJy/beam rms and a resolution of 13’’. Our partial observations have achieved an image sensitivity of approximately 140 uJy, with a goal of reaching 30 uJy using existing data. These advanced techniques are propelling the joint studies of cosmology and radio astronomy to new heights, and with the emergence of the Square Kilometre Array (SKA), the future of this field looks exceptionally promising.

The Square Kilometre Array (SKA) promises groundbreaking advances in key scientific areas, including ultra-sensitive continuum imaging and probing the cosmos through redshifted spectral lines from the epochs of cosmic dawn and reionization. However, achieving these ambitious goals requires overcoming significant challenges, particularly at low frequencies. These include ionospheric distortions, wide fields of view, complex antenna layouts, and the massive data volumes generated—all of which make calibration and imaging exceptionally difficult.

While precursor instruments have demonstrated steady progress and highlighted SKA’s immense scientific potential, the complexity of the SKA's mission demands innovative, independent approaches to deliver robust results. This unique landscape presents unparalleled opportunities for developing novel methods to address calibration and imaging challenges at scale.

In this talk, I will showcase promising advancements in tools designed for calibration and imaging. These methods offer a glimpse into how we can tackle SKA's challenges and harness its full potential, paving the way for transformative discoveries in astronomy.

I will present recent progress in constraining the 21-cm power spectrum of neutral hydrogen from the Epoch of Reionization (EoR) using the Low-Frequency Array (LOFAR), bringing us increasingly closer to the sensitivity levels predicted by standard astrophysical models. Achieving deeper limits requires not only adding additional data but also addressing systematic errors, including instrumental and ionospheric effects, as well as mitigating radio-frequency interference. In this talk, I will highlight the rapid advancements our team has achieved in tackling these obstacles, with a particular focus on the largest remaining challenge: direction-dependent gain calibration. Additionally, I will discuss the implications of our latest results, which provide new constraints on the intergalactic medium (IGM) during the EoR, derived from our deepest power-spectrum measurements across three redshifts.