Photon decaying in de Sitter universe

The interaction between three photons is studied in de Sitter ambient space formalism. As a special case, the half harmonic generator is considered, i.e., one photon decays to two same-energy photons. The scattering matrix elements are presented which define the indirect gravitational effect on quantum field theory. The null curvature limit of scattering matrix is obtained for comparing it with its Minkowskian counterpart. The Hamiltonian of this interaction, in Minkowski space–time, was presented by using the quantum vacuum fluctuation in the one-loop approximation.