Linearised gravitational radiation in de Sitter spacetime at all multipole orders

Abstract

We derive the linearised gravitational waves generated by a localised matter source in the Poincare patch of de Sitter spacetime at arbitrary multipole order. The linearised de Sitter problem is mapped exactly to an auxiliary flat-space problem in harmonic gauge, with a conserved source built from the physical stress tensor. This allows us to use the multipole expansion of Damour and Iyer verbatim, and yields the exterior metric at all orders in terms of two families of radiative multipole moments given as explicit integrals of the physical stress tensor. The de Sitter tail is absorbed entirely into the auxiliary stress tensor, so that neither the moments nor the canonical exterior metric carry an integral over the past history of the source. As a check, we recover the known quadrupolar metric: in the quadrupolar truncation it is our canonical field up to a residual gauge transformation, which we construct explicitly.