de Sitter Corrections to Gravitational Wave Memory

Abstract: In this work, we compute the gravitational wave displacement and spin memory effects in de Sitter spacetime. Gravitational waves in asymptotically flat spacetimes are described by the Bondi-Sachs framework, where radiation at null infinity is tied to the BMS group, and memory appears as permanent changes in the geometry. This formalism becomes more complicated when asymptotic flatness is not guaranteed. With a positive cosmological constant, future infinity is spacelike rather than null, and the decay of the fields differs qualitatively from the flat case. The Bondi-Sachs methods adapted to a positive cosmological constant show that the asymptotic symmetry algebra reduces to time translations and rotations, and that the balance equations for charges and fluxes take a modified form. Our calculation at leading order yields flux-balance relations for displacement and spin memory directly in terms of the cosmological constant Lambda and Bondi-Sachs data. We also find that the cosmological constant mixes spherical-harmonic modes of the memory potentials, producing a (3,0) component in displacement memory and a (2,0) component in spin memory.