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New boundary conditions are imposed on the familiar cylindrical gravitationalwave vacuum spacetimes. The new spacetime family represents cylindrical wavesin a flat expanding (Kasner) universe. Space sections are flat and nonconicalwhere the waves have not reached and wave amplitudes fall off more rapidly thanthey do in Einstein-Rosen solutions, permitting a more regular null inifinity.Comment: Minor corrections to references. A note added in proo

Cylindrical gravitational waves in expanding universes: Models for waves from compact sources