Axial gravitational waves in FLRW cosmology and memory effects

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.

Figure 1

Space-time diagram showing the propagation of the considered gravitational pulse (${\eta }_{wf}=r-r_2+{\eta }_0$). The dashed line shows the integration contour for the integral in (16).