Gravitons and light cone fluctuations

Gravitons in a squeezed vacuum state, the natural result of quantum creation in the early Universe or by black holes, will introduce metric fluctuations. These metric fluctuations will introduce fluctuations of the light cone. It is shown that when the various two-point functions of a quantized field are averaged over the metric fluctuations, the light cone singularity disappears for distinct points. The metric-averaged functions remain singular in the limit of coincident points. The metric-averaged retarded Green’s function for a massless field becomes a Gaussian which is nonzero both inside and outside of the classical light cone. This implies some photons propagate faster than the classical light speed, whereas others propagate slower. The possible effects of metric fluctuations upon one-loop quantum processes are discussed and illustrated by the calculation of the one-loop electron self-energy.