Energy of gravitational radiation in the de Sitter universe at I+ and at a horizon

Abstract

In this note, we investigate outcomes of a symplectic formula for the gravitational wave charges in general relativity linearized around the de Sitter spacetime. We derive their explicit form at ${\mathcal{I}}^{+}$ in the Bondi frame, compare with the connected Noether expression, and analyze their gauge dependence, which allows us to fix unambiguously the boundary terms. We also discuss the minimal requirements needed to be imposed on the initial data in order to have finite values of charges. Furthermore, we analyze the transformation laws of the energy upon the action of the de Sitter group and discuss their physical interpretation. Finally, we calculate their flux through a cosmological horizon instead of ${\mathcal{I}}^{+}$. We show that in the limit $\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}0$, one recovers the Trautman-Bondi formula, strengthening a recent proposal that one should choose a null surface as a more natural boundary for the astrophysical systems in the presence of the cosmological constant.