Photon decaying in de Sitter universe
Y. Ahmadi, M. V. Takook
TL;DR
This work investigates the decay of a photon into two photons within de Sitter ambient-space quantum field theory, capturing indirect gravitational effects through the three-photon S-matrix at leading order. It derives the interaction Hamiltonian ${\cal H}_{int}=-qH\bar{\Psi}\gamma^4\cancel{x}\cancel{{\cal A}}\Psi$ and computes the third-order S-matrix ${\cal S}^{(3)}$ via Wick contractions with the spinor two-point function ${\bf S}(x,x')$, showing how curvature enters the amplitude through these correlators and polarization structures. In the null-curvature limit $H\to0$, the dS expressions reduce to the Minkowski counterparts, with ${\chi}^{dS}$ converging to the flat-space triple-photon amplitude characterized by a momentum-conserving delta function $\delta^4(k-k'-k'')$ and a standard loop integral. The results provide a framework to quantify curvature-induced corrections in QFT and suggest numerical evaluation of the full ${\cal S}^{(3)}$ as well as future inclusion of bulk-curvature effects. This work thus connects QFT in curved backgrounds to observable photon-photon interactions and validates the consistency with flat-space QFT in the appropriate limit.
Abstract
The interaction between three photons is studied in de Sitter ambient space formalism. As a special case the half harmonic generator is considered, {\it 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.