Cosmological Horizon and the Quadrupole Formula in de Sitter Background

An important class of observables for gravitational waves consists of the fluxes of energy, momentum and angular momentum carried away by them and are well understood for weak gravitational waves in Minkowski background. In de Sitter background, the future null infinity, $\mathcal{J}^+$, is space-like which makes the meaning of these observables subtle. A spatially compact source in de Sitter background also provides a distinguished null hypersurface, its {\em cosmological horizon}, $\mathcal{H}^+$. For sources supporting the short wavelength approximation, we adopt the Isaacson prescription to define an effective gravitational stress tensor. We show that the fluxes computed using this effective stress tensor can be evaluated at $\mathcal{H}^+$, match with those computed at $\mathcal{J}^+$ and also match with those given by Ashtekar et al at $\mathcal{J}^+$ {{\em at a coarse grained level}}.