Effect of a cosmological constant on propagation of vacuum polarized photons in stationary spacetimes

TL;DR

This paper investigates how a positive cosmological constant influences vacuum polarized photon propagation in stationary spacetimes, revealing potential effects in static de Sitter cosmic string and Kerr-de Sitter backgrounds.

Contribution

It demonstrates that the cosmological constant can affect photon propagation in stationary spacetimes, extending previous findings to new geometries like the static de Sitter cosmic string and Kerr-de Sitter.

Findings

Positive cosmological constant affects photon propagation in stationary spacetimes.

Effects are observed for physical polarizations in specific geometries.

Results are consistent with the polarization sum rule.

Abstract

Consideration of vacuum polarization in quantum electrodynamics may affect the momentum dispersion relation for photons for a non-trivial background, due to appearance of curvature dependent terms in the effective action. We investigate the effect of a positive cosmological constant $\Lambda$ on this at one loop order for stationary $\Lambda$-vacuum spacetimes. To the best of our knowledge, so far it has been shown that $\Lambda$ affects the propagation in a time dependent black hole spacetime. Here we consider the static de Sitter cosmic string and the Kerr-de Sitter spacetime to show that there can be some non-vanishing effect due to $\Lambda$ for physical polarizations. Consistency of these results with the polarization sum rule is discussed.