Gravitational waves in a de Sitter universe

TL;DR

This paper extends the Bondi-Sachs formalism to linearized gravitational waves in de Sitter space, analyzing energy conservation and observer dependence in a universe with positive cosmological constant.

Contribution

It provides exact linearized solutions for gravitational waves in de Sitter spacetime and explores energy conservation for different classes of observers.

Findings

Gravitational wave energy conservation depends on observer acceleration.

Exact solutions are constructed within the Bondi-Sachs framework.

Energy measured by inertial observers generally does not conserve.

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.