Gravitational wave memory in conformally flat spacetimes

We study the gravitational wave memory effect in spacetimes related to flat space by a conformal transformation. The discussion is general but the gravitational wave length scale is assumed to be small compared with the background curvature radius. The general formulas are applied to Friedmann-Robertson-Walker metrics of all spatial curvatures. The effect of new terms stemming from spatial curvature is potentially detectable in future gravitational wave measurements.
27 pages, 1 figure; v2: a new paragraph added at the beginning of Sec. 3, reference to Fig. 1 added in the text, typos corrected, published version