Electromagnetic Field in de Sitter Expanding Universe: Majorana--Oppenheimer Formalism, Exact Solutions in non-Static Coordinates

TL;DR

This paper applies the Majorana--Oppenheimer formalism to derive exact electromagnetic solutions in a non-static de Sitter universe, revealing quantized mode dependence on time and connecting to the Duffin-Kemmer-Petiau formalism.

Contribution

It introduces a novel application of the Majorana--Oppenheimer formalism to non-static de Sitter space, deriving exact solutions and linking to Duffin-Kemmer-Petiau theory.

Findings

Quantized separation parameter in electromagnetic modes

Exact solutions for electromagnetic fields in de Sitter space

Connection established between complex vector and DKP formalisms

Abstract

Tetrad-based generalized complex formalism by Majorana--Oppenheimer is applied to treat electromagnetic field in extending de Sitter Universe in on-static spherically-symmetric coordinates. With the help of Wigner D-functions, we separate angular dependence in the complex vector field E_{j}(t,r)+i B_{j}(t,r) from (t,r)-dependence. The separation parameter arising here instead of frequency \omega in Minkowski space-time is quantized, non-static geometry of the de Sitter model leads to definite dependence of electromagnetic modes on the 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.