Axial gravitational waves in FLRW cosmology and memory effects

摘要

We show initial data for gravitational axial waves that are twice differentiable but that are not C~2. They generate wave pulses that interact with matter in the radiation cosmological era. This forces the radiation matter to rotate. This rotation is permanent-it persists after the passage of the gravitational pulse. The observed inhomogeneities of the cosmic microwave background radiation put a bound onto discontinuities of superhorizon metric perturbations. We explicitly show that a class of smooth initial metrics that are at least C~2 gives rise to gravitational wave pulses that do not interact with the background during the radiation epoch.