The effects of the antenna power pattern uncertainty within a global 21 cm experiment

Measuring the redshifted sky-averaged neutral hydrogen 21 cm signal with a wide-band antenna operating at metre wavelengths can probe the thermal history of the Universe and the first star and galaxy formation during the Cosmic Dawn. Measurement of this ‘global 21 cm’ signal is extremely challenging due to foreground signals that are orders of magnitude brighter than the cosmological signal, which must be modelled and removed first. The Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) aims to improve this process by simultaneously fitting the full posterior distribution of both the cosmological and foreground signals with Bayesian inference. The method, however, relies on an informed prior; partially derived from a simulated antenna power pattern. This simulated antenna power pattern will differ from the true antenna power pattern of the deployed instrument, and the impact of this uncertainty is unknown. We investigate this problem by forward modelling mock data with different levels of power pattern uncertainty through the REACH pipeline. We construct perturbed antenna power patterns through truncation of a singular-value-decomposed simulated power pattern; using one to generate mock observation data and the others to inform the prior. The power pattern uncertainty is quantified as ΔD, the absolute mean of the difference between the original and perturbed power patterns. Comparing the evidence and root-mean-square error we find that ΔD better than −35 dB, equivalent to millimetre accuracy in the antennas dimensions, is necessary for confident detection of the global signal. We discuss potential solutions to achieve this high level of accuracy.