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Observations of the 21-cm line from primordial hydrogen promise to be one of the best tools to study the early epochs of the Universe: the Dark Ages, the Cosmic Dawn, and the subsequent Epoch of Reionization. In 2018, the EDGES experiment caught the attention of the cosmology community with a potential detection of an absorption feature in the sky-averaged radio spectrum centred at 78 MHz. The feature is deeper than expected, and, if confirmed, would call for new physics. However, different groups have re-analyzed the EDGES data and questioned the reliability of the signal. The Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) is a sky-averaged 21-cm experiment aiming at improving the current observations by tackling the issues faced by current instruments related to residual systematic signals in the data. The novel experimental approach focuses on detecting and jointly explaining these systematics together with the foregrounds and the cosmological signal using Bayesian statistics. To achieve this, REACH features simultaneous observations with two different antennas, an ultra wideband system (redshift range 7.5 to 28), and a receiver calibrator based on in-field measurements. Simulated observations forecast percent-level constraints on astrophysical parameters, potentially opening up a new window to the infant Universe., Comment: Publication date: 21 July 2022

Following the reported detection of an absorption profile associated with the 21~cm sky-averaged signal from the Cosmic Dawn by the EDGES experiment in 2018, a number of experiments have been set up to verify this result. This paper discusses the design process used for global 21~cm experiments, focusing specifically on the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH). This experiment will seek to understand and compensate for systematic errors present using detailed modelling and characterization of the instrumentation. There is detailed the quantitative figures of merit and numerical modelling used to assist the design process of the REACH dipole antenna (one of the 2 antenna designs for REACH Phase I). This design process produced a 2.5:1 frequency bandwidth dipole. The aim of this design was to balance spectral smoothness and low impedance reflections with the ability to describe and understand the antenna response to the sky signal to inform the critically important calibration during observation and data analysis., Comment: 32 pages, 30 figures, to be submitted to the Journal of Astronomical Instrumentation

Detection of millikelvin-level signals from the 'Cosmic Dawn' requires an unprecedented level of sensitivity and systematic calibration. We report the theory behind a novel calibration algorithm developed from the formalism introduced by the EDGES collaboration for use in 21-cm experiments. Improvements over previous approaches are provided through the incorporation of a Bayesian framework and machine learning techniques such as the use of Bayesian evidence to determine the level of frequency variation of calibration parameters that is supported by the data, the consideration of correlation between calibration parameters when determining their values and the use of a conjugate-prior based approach that results in a fast algorithm for application in the field. In self-consistency tests using empirical data models of varying complexity, our methodology is used to calibrate a 50 $\Omega$ ambient-temperature load. The RMS error between the calibration solution and the measured temperature of the load is 8 mK, well within the 1$\sigma$ noise level. Whilst the methods described here are more applicable to global 21-cm experiments, they can easily be adapted and applied to other applications, including telescopes such as HERA and the SKA., Comment: 9 pages, 9 figures