Generalization of the quadruple formula for the energy of gravitational radiation in de Sitter spacetime

We study gravitational radiation produced by time-changing matter source in de Sitter spacetime. We consider a cosmological Killing horizon instead of the conformal boundary used in the radiation theory in the Minkowski spacetime. The energy of the radiation passing through the horizon is derived. Our result takes the form of a generalized quadrupole formula expressed in terms of the mass and pressure quadrupole p ffiffiffimoments and is written explicitly up to the first order in A . The zeroth-order term recovers the famous Einstein's quadrupole formula obtained for the perturbed Minkowski spacetime, whereas the first-order term is a new correction.