Electromagnetic field on de sitter expanding Universe: Majorana–Oppenheimer Formalism, exact solutions in non-static coordinates

Abstract

Tetrad-based generalized complex formalism by Majorana–Oppenheimer is applied to treat an electromagnetic field on expanding de Sitter Universe in non-static spherically-symmetric coordinates. With the help of the Wigner D-functions, we separate angular dependence in the complex vector field Ej(t, r)+iBj(t, r) from (t, r)-dependence. The separation parameter arising here instead of frequency ω in Minkowski space-time is quantized, non-static geometry of the de Sitter model leads to definite dependence of electromagnetic modes on time variable.Relation of 3-vector complex approach to 10-dimensional Duffin–Kemmer–Petiau formalism is considered. On this base, the electromagnetic waves of magnetic and electric type have been constructed in both approaches. In Duffin–Kemmer–Petiau approach, there are constructed gradient-type solutions in Lorentz gauge.