Measuring the Cosmological 21 cm Monopole with an Interferometer

A measurement of the cosmological 21 cm signal remains a promising but as-of-yet unattained ambition of radio astronomy. A positive detection would provide direct observations of key unexplored epochs of our cosmic history, including the cosmic dark ages and reionization. In this paper, we concentrate on measurements of the spatial monopole of the 21 cm brightness temperature as a function of redshift (the "global signal"). Most global experiments to date have been single-element experiments. In this paper, we show how an interferometer can be designed to be sensitive to the monopole mode of the sky, thus providing an alternate approach to accessing the global signature. We provide simple rules of thumb for designing a global signal interferometer and use numerical simulations to show that a modest array of tightly packed antenna elements with moderately sized primary beams (full-width-half-max of $\sim$40$^\circ$) can compete with typical single-element experiments in their ability to constrain phenomenological parameters pertaining to reionization and the pre-reionization era. We also provide a general data analysis framework for extracting the global signal from interferometric measurements (with analysis of single-element experiments arising as a special case) and discuss trade-offs with various data analysis choices. Given that interferometric measurements are able to avoid a number of systematics inherent in single-element experiments, our results suggest that interferometry ought to be explored as a complementary way to probe the global signal.