Scalar pair production in a magnetic field in de Sitter universe

The production of scalar particles by the dipole magnetic field in de Sitter expanding universe is analyzed. The amplitude and probability of transition are computed using perturbative methods. A graphical study of the transition probability is performed obtaining that the rate of pair production is important in the early universe. Our results prove that in the process of pair production by the external magnetic field the momentum conservation law is broken. We also found that the probabilities are maximum when the particles are emitted perpendicular to the direction of magnetic dipole momentum. The total probability is computed and is analysed in terms of the angle between particles momenta