In cosmology, recombination refers to the epoch during which charged electrons and protons first became bound to form electrically neutral hydrogen atoms.
[2] The word "recombination" is misleading, since the Big Bang theory does not posit that protons and electrons had been combined before, but the name exists for historical reasons since it was named before the Big Bang hypothesis became the primary theory of the birth of the universe.
At 10−6 seconds, the Universe had expanded and cooled sufficiently to allow for the formation of protons: the hadron epoch.
Eventually, the universe cooled to the point that the radiation field could not immediately ionize neutral hydrogen, and atoms became energetically favored.
[3] The fraction of free electrons and protons as compared to neutral hydrogen decreased to a few parts in 10000.
Once photons decoupled from matter, they traveled freely through the universe without interacting with matter and constitute what is observed today as cosmic microwave background radiation (in that sense, the cosmic background radiation is infrared and some red black-body radiation emitted when the universe was at a temperature of some 3000 K, redshifted by a factor of 1100 from the visible spectrum to the microwave spectrum).
[4] The microwave background is a blackbody spectrum representing the photons present at recombination, shifted in energy by the expansion of the universe.
The thermal energy at the peak of the blackbody spectrum is the Boltzmann constant, kB, times the temperature,
with energy E sufficient to ionize hydrogen is the total density times a factor from the equilibrium Boltzmann distribution:
The cosmic ionization history is generally described in terms of the free electron fraction xe as a function of redshift.
The relative abundance of free electrons, protons and neutral hydrogen is then given by the Saha equation: where me is the mass of the electron, kB is the Boltzmann constant, T is the temperature, ħ is the reduced Planck constant, and EI = 13.6 eV is the ionization energy of hydrogen.
[5] Charge neutrality requires ne = np, and the Saha equation can be rewritten in terms of the free electron fraction xe: All quantities in the right-hand side are known functions of z, the redshift: the temperature is given by T = (1 + z) × 2.728 K,[6] and the total density of hydrogen (neutral and ionized) is given by np + nH = (1 + z)3 × 1.6 m−3.
Solving this equation for a 50 percent ionization fraction yields a recombination temperature of roughly 4000 K, corresponding to redshift z = 1500.
In 1968, physicists Jim Peebles[7] in the US and Yakov Borisovich Zel'dovich and collaborators[8] in the USSR independently computed the non-equilibrium recombination history of hydrogen.
Accounting for these processes, the recombination history is then described by the differential equation where αB is the "case B" recombination coefficient to the excited states of hydrogen, βB is the corresponding photoionization rate and E21 = 10.2 eV is the energy of the first excited state.
Note that the second term in the right-hand side of the above equation can be obtained by a detailed balance argument.
The equilibrium result given in the previous section would be recovered by setting the left-hand side to zero, i.e. assuming that the net rates of recombination and photoionization are large in comparison to the Hubble expansion rate, which sets the overall evolution timescale for the temperature and density.
However, C αB np is comparable to the Hubble expansion rate, and even gets significantly lower at low redshifts, leading to an evolution of the free electron fraction much slower than what one would obtain from the Saha equilibrium calculation.
The simple effective three-level atom model described above accounts for the most important physical processes.
Due to the importance of recombination for the precise prediction of cosmic microwave background anisotropies,[10] several research groups have revisited the details of this picture over the last two decades.
[11][12] Helium nuclei are produced during Big Bang nucleosynthesis, and make up about 24% of the total mass of baryonic matter.
Prior to recombination, photons were not able to freely travel through the universe, as they constantly scattered off the free electrons and protons.
[16] For this reason, recombination is closely associated with the last scattering surface, which is the name for the last time at which the photons in the cosmic microwave background interacted with matter.
[17] However, these two events are distinct, and in a universe with different values for the baryon-to-photon ratio and matter density, recombination and photon decoupling need not have occurred at the same epoch.