Gravitational waves in a de Sitter universe

TL;DR

This work extends the Bondi-Sachs formalism to linearized gravitational waves about a de Sitter background, constructing exact perturbative solutions and the corresponding GW field and energy as seen by distant observers. By using ψ4 as a gauge-invariant descriptor, the authors show how GW energy flux depends on observer motion, with energy conservation holding only for a special class of accelerated observers rather than inertial ones. They derive the leading GW behavior for an ℓ=2 mode and adapt the equal-mass binary calculation to de Sitter, finding only negligible corrections for realistic systems. These results clarify how a positive cosmological constant alters GW generation and detection concepts, while highlighting important subtleties in defining GW energy in curved backgrounds and setting the stage for future mass-loss formalisms in de Sitter spacetimes.

Abstract

The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is constructed, leading to a determination of the energy measured by such observers. It is found that gravitational wave energy conservation does not normally apply to inertial observers, but that it can be formulated for a class of accelerated observers, i.e. with worldlines that are timelike but not geodesic.