Astroparticle Physics

11.3 Formation of the CMB 23311.3 Formation of the CMB“The old dream of wireless communicationthrough space has now been realizedin an entirely different manner thanmany had expected. The cosmos’ shortwaves bring us neither the stock marketnor jazz from different worlds. With softnoises they rather tell the physicists ofthe endless love play between electronsand protons.”Albrecht UnsöldAt very early times, any protons and electrons that managedto bind together into neutral hydrogen would be dissociatedvery quickly by collision with a high-energy photon. As thetemperature decreased, the formation of hydrogen eventuallybecame possible and the universe transformed from anionized plasma to a gas of neutral atoms; this process iscalled recombination. The reduction of the free electron densityto almost zero meant that the mean free path of a photonsoon became so long that most photons have not scatteredsince. This is called the decoupling of photons from matter.By means of some simple calculations one can estimatewhen recombination and decoupling took place.Neutral hydrogen has an electron binding energy of13.6 eV and is formed through the reactionrecombination: creationof hydrogen atomsdecoupling of photonsfrom matterp + e − → H + γ. (11.6)Naïvely one would expect the fraction of neutral hydrogento become significant when the temperature drops below13.6 eV. But because the baryon-to-photon ratio η ≈5 × 10 −10 is very small, the temperature must be significantlylower than this before the number of photons withE > 13.6 eV is comparable to the number of baryons.(This is the same basic argument for why deuterium productionbegan not around T = 2.2 MeV, the binding energyof deuterium, but rather much lower.) One finds thatthe numbers of neutral and ionized atoms become equal ata recombination temperature of T rec ≈ 0.3 eV (3500 K). Atthis point the universe transforms from an ionized plasma toan essentially neutral gas of hydrogen and helium.It can be estimated when recombination took place bycomparing the temperature of the CMB one observes today,T 0 ≈ 2.73 K, to the value of the recombination temperatureT rec ≈ 0.3 eV. Recall from Sect. 9.2.4 that the wavelengthrecombination temperatureestimationof the recombination era