Photon decoupling occurs when the Thomson-scattering rate drops below the Hubble expansion rate. Photons then free stream and form the cosmic microwave background.
The physical Thomson scattering rate equals the inverse photon mean scattering time. Comparing it with the Hubble parameter gives a local approximate decoupling criterion. A more precise last-scattering temperature is obtained from optical depth and the visibility maximum; these conventions need not give exactly the same temperature.
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