Hydrogen recombination in the early Universe in the presence of a magnetic field

Hydrogen recombination in the early Universe in the presence of a magnetic field is studied. An equation for the temperature of recombination in the presence of a magnetic field is derived. Limiting cases of weak and strong fields are considered. It is demonstrated that there exists a critical magnetic field, above which the system stays in the phase of atomic hydrogen for all temperatures. The relative shift of the temperature of recombination in the presence of a magnetic field is estimated and it is demonstrated that this shift is small.