Recombination is the (inappropriate) name given to the formation of neutral hydrogen from the previously free protons and electrons. Formation of neutral helium atoms has occurred somewhat earlier. Hydrogen recombination takes place mostly between 180,000 years and 350,000 years, when the temperature falls from 4,300 K to 3070 K and the free electron and free proton concentrations fall from 99% to 1%.
Hydrogen recombination ceases at a temperature of 2574 K, at 462,000 years, when the numbers of remnant free protons and electrons are a fraction 7 x 10^-5 of their initial numbers.
Prior to recombination the universe is opaque due to the free electrons interacting with the photons. The universe becomes transparent as the number of free electrons falls during recombination. Transparency of the universe occurs at ~300,000 years, when the temperature is ~3320 K, and the remnant fraction of free electrons is ~5.7%. Hence, transparency occurs during the period of most active hydrogen recombination, and before recombination is complete.
If the photon:baryon ratio were reduced by more than a factor of ten, the universe would remain opaque during the period of most active hydrogen recombination (i.e. whilst 99% of the neutral hydrogen were being formed). If the photon:baryon ratio were increased by more than a factor of ten, the universe would already be transparent when the period of most active hydrogen recombination starts (i.e. before the neutral hydrogen level reaches 1%). Hence, there is a coincidence between the time of recombination and the time of transparency which depends upon the specific value for the photon:baryon ratio which pertains to this universe. It is not clear whether this coincidence is anthropically constrained, perhaps due to its implications for structure formation.
If the photon:baryon ratio were 1000 times smaller (i.e. 1000 times more baryons) then the universe would remain opaque forever. This is because the concentration of remnant free electrons when the recombination reaction freezes-out due to cosmic expansion would be large enough to prevent photons circumnavigating the universe uninterrupted.
Structure formation is likely to be prevented whilst the universe remains opaque due to the radiation pressure support which would prohibit gravitational collapse. Hence, there is an anthropic reason for the photon:baryon ratio being greater than 2 x 10^6 (i.e., less than 1/1000th of its actual value). This consistutes a very weak coincidence (single-sided, and weaker than Type D).
The coincidence between the time of recombination and the time of transparency potentially constitutes a double-sided Type D coincidence in the value of the photon:baryon ratio. However, it is not clear that this coincidence is actually needed for anything.
