Let’s begin with the pioneering way of estimating BAO size via galaxy clustering. Picking a random galaxy one can estimate the probability of finding another galaxy within a given distance — this is called the two correlation function — and it is related to the Fourier space power spectrum of the galaxy distribution. At the comoving separation coincident to the sound horizon radius (at that moment in the history of the universe) an excess (graphically a “bump”) should be present, see figure below.
Detection of BAO using data of Sloan Digital Sky Survey luminous red galaxies: the bump in the galaxy correlation function appears at 100 h⁻¹ Mpc scale. Adapted from Eisenstein et al. (2005).
In order to pinpoint these wiggles, the matter power spectrum has to be known at a very high level of precision. In the case of detecting matter via HI emission, the procedure is similar, with the correlation function being obtained by measuring the HI fluctuations between two points in the sky.
Atomic hydrogen, through the emission line at wavelength of 21 cm (frequency of 1.4 GHz), is detected in the region of the electromagnetic spectrum corresponding to the radio. Note that 21 cm is the wavelength in the reference frame, the farther the source is, the more “redshifted” the line will be, and so will be detected at higher wavelengths, or what is equivalent, at lower frequencies.
At those (low) frequencies, the beam of the radio telescopes is quite broad, which is perfect considering that the goal is to detect the mean signal from many galaxies. There are several broad beam radio telescopes around the world. Nevertheless they can not detect BAO. Why?