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Recombination is the time in the universe when free electrons and protons combined into neutral hydrogen. One of the most important features of this transition is that after recombination the photons "decoupled" from matter. I believe decoupling refers to the fact that the probability that a given photon scatters off an atom between the time of decoupling and today is negligible. That is, after decoupling the photons travel on straight lines without interacting. This gives rise to the Cosmic Microwave Background: basically a snapshot of the universe at the time of recombination/decoupling.

My question is about "21cm Cosmology" in light of this decoupling. Neutral hydrogen can absorb a photon with a wavelength of 21cm. The detection principle is that some of the photons from the early universe are absorbed by neutral hydrogen on their way to us. We detect this as a deficit of photons at particular frequencies.

But this seems to contradict the idea of "decoupling". If the photons are decoupled it means they don't meet any atoms as they travel to us. But then how are some of them absorbed by the neutral hydrogen?

Any clarification of my clearly muddled understanding is appreciated.

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The term "decoupling" is just a very good approximation for most frequencies. For frequencies higher than Lyman-alpha (Doppler broadened) the photons took longer to decouple. This is partly because the scattering/interaction cross-section for these transitions are very high.

For the $21\operatorname{cm}$ line, in contrast, my understanding is that the cross section is relatively low, though I can't find any data substantiating this. My understanding is that the only reason we can even detect the $21\operatorname{cm}$ line is because of the sheer quantity of neutral hydrogen in the universe. So, even though the neutral hydrogen will scatter $21\operatorname{cm}$ hydrogen, even detectably so, it isn't a strong coupling.

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