What the early hydrogen sends us
A hydrogen atom can flip the spin of its electron and emit or absorb a radio wave 21 centimetres long, at 1420 megahertz. Hydrogen gas filled the space between the first galaxies, so this line lets us map gas that never formed stars. On the way to us the universe expands and stretches the wave. Light from hydrogen at redshift eight, when every distance was nine times smaller than today, arrives at about 159 megahertz, a little above the FM radio band.
The gas does not shine on its own terms. We see it against the microwave background, the oldest light in the universe. Where the hydrogen is colder than that background it absorbs and looks darker; where it is warmer it adds a little glow. The first starlight decides how closely the atoms follow the gas temperature, and X-rays from early black holes and stellar remnants can warm the gas. The resulting contrast is only tens of thousandths of a kelvin. Furlanetto, Oh and Briggs 2006, §2.3 and §3.2
Why the sky drowns it
Fast electrons spiralling in the magnetic field of the Milky Way fill the whole sky with radio emission, called synchrotron radiation. At these frequencies even the quietest patches of sky are a couple of hundred kelvin bright. A common rule of thumb gives about 180 kelvin at 180 megahertz, rising towards lower frequencies. Furlanetto, Oh and Briggs 2006, §9.1.1 At 159 megahertz that is about 250 kelvin, against a hydrogen contrast near 0.02 kelvin. Radio astronomers call everything in front of the signal the foreground.
Making a better map does not help by itself. The foreground sits in the same direction as the hydrogen and arrives at the same frequencies.
The one difference that saves the search
The foreground is smooth in frequency. Synchrotron emission at 159 megahertz and at 160 megahertz comes from the same electrons in our galaxy, so the two brightnesses differ by a small, predictable amount. Hydrogen behaves differently. A one-megahertz step in frequency moves the line of sight about 50 million light-years through the early universe, into a different patch of denser or thinner gas. So the hydrogen part of the spectrum is bumpy.
Think of a loud, steady hum with a faint crackle on top. You cannot turn the hum down, but you can listen only for changes that happen faster than the hum ever changes. Radio arrays do the same thing with frequency instead of time.
How a pair of dishes sorts the sky
An interferometer combines signals from two dishes a fixed distance apart. A wave from a source off to one side reaches one dish a little before the other. That timing difference is called the delay. It is largest for a source on the horizon, where it equals the dish spacing divided by the speed of light: about 49 billionths of a second for dishes 14.6 metres apart. Parsons et al. 2012, §2.1
Sort the measured spectrum by delay and a smooth foreground stays at short delays, inside that horizon limit. The bumpy hydrogen spreads out to long delays too. Longer baselines have longer horizon delays, so on a chart of delay against dish spacing the foreground fills a wedge, with a cleaner window above it.
Real instruments blur the edge. Echoes in cables, the finite frequency band and a dish whose sensitivity pattern changes with frequency all add structure to the spectrum and push some foreground past the horizon. HERA's first analysis subtracted no foreground model. It left a safety margin of 200 billionths of a second beyond the horizon and used only the delays above it. HERA Collaboration 2022, §4.3
What HERA has found so far
HERA has not yet detected the signal. From 18 nights of data it set upper limits: at redshift 7.9, for patterns that repeat about every 160 million light-years, the hydrogen brightness fluctuations must be smaller than about 31 thousandths of a kelvin. At redshift 10.4 the limit is about 96 thousandths of a kelvin. HERA Collaboration 2022, §4.4
Even an upper limit says something. If the gas had never been warmed after the Big Bang, it would be very cold by redshift eight and would cast a deep, patchy shadow. The HERA team reports that, under standard models of early galaxies, its limits disfavour such a cold universe. Something had already warmed the gas above the temperature it would reach by cooling alone. HERA Collaboration 2022, §1
The course that follows works through each step with numbers: why the hydrogen glows or darkens, how one baseline separates the foreground and how a published limit is built.