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

TL;DR

This paper analyzes gravitational wave energy in de Sitter spacetime, deriving explicit charge formulas at scri and horizons, comparing different expressions, and exploring their physical and gauge properties.

Contribution

It provides explicit formulas for gravitational wave charges in de Sitter space at scri and horizons, clarifies gauge dependence, and connects with the Trautman--Bondi energy in the zero cosmological constant limit.

Findings

Derived explicit charge formulas at scri in Bondi frame.

Compared symplectic and Noether expressions for charges.

Showed flux at the horizon recovers Trautman--Bondi formula as  o 0.

Abstract

In this note we investigate outcomes of a symplectic formula for the gravitational waves charges in the general relativity linearized around the de Sitter spacetime. We derive their explicit form at {\it scri} in the Bondi frame, compare with the connected Noether expression and analyze their gauge dependence which allows us to fix unambiguously boundary terms. We also discuss minimal requirements needed to impose on initial data to have finite values of charges. Furthermore, we analyze transformation laws of the energy upon the action of the de Sitter group and discuss its physical interpretation. Finally, we calculate its flux through a cosmological horizon instead of {\it scri}. We show that in the limit $\Lambda \to 0$, one recovers Trautman--Bondi formula strengthening 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.