de Sitter Corrections to Gravitational Wave Memory

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. We calculate the leading order corrections due to de Sitter spacetime. At leading order, this yields flux-balance relations for displacement and spin memory directly in terms of the cosmological constant and Bondi-Sachs data. We find that the cosmological constant corrections for the leading term are of the order {\Lambda} for both displacement and spin memory. These corrections are, as expected, too small to be detected by any current or future gravitational wave observatories.