Maxwell field in spatially flat FLRW space-times

Abstract

Abstract The classical and quantum theory of the Maxwell free field (or perturbation) minimally coupled to the gravity of local-Minkowskian spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) space-times is constructed in conformal local charts (herein called frames) where the Maxwell equations have the same form as in special relativity. Taking into account that the conformal coordinates cannot be measured directly, all the obtained results are transformed in physical frames, with cosmic time and space coordinates of Painlevé type, where these may take on a physical meaning. In these frames, the Maxwell theory is equivalent to the electrodynamics in flat macroscopic media whose constitutive equations predict magnetoelectric type effects interpreted here as a geometric induction. The given example is of a system of static charges giving rise simultaneously to time-dependent electric and magnetic fields that can be measured in physical frames. The quantization of the Maxwell free field in these manifolds is performed in a canonical manner using the momentum-helicity basis. The propagators in conformal and physical frames and the principal one-particle operators are written down. It is shown that this approach reveals a new behaviour of the one-particle wave packets during propagation and specific effects produced by the apparent horizons of the observers staying at rest in their proper physical frames.