Asymptotics with a positive cosmological constant: II. Linear fields on de Sitter space-time

Abstract

Linearized gravitational waves in de Sitter space-time are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity. Specifically: i) In the exact theory, the intrinsic geometry of $\scri$ is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from $\Diff$ to the de Sitter group. Our {results show explicitly} that this condition is physically unreasonable; ii) We obtain expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at $\scrip$; iii) We argue that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy; and, finally iv) We demonstrate that the flux formulas reduce to the familiar ones in Minkowski space-time in spite of the fact that the limit $Λ\to 0$ is discontinuous (since, in particular, $\scri$ changes its space-like character to null in the limit).

22 pages, 4 figures. Added two clarifications in section V (on the use of the Poincaré patch and on the relation with Friedrich's result [19] in full GR). We thank the referee for bringing to our attention Ref [19]. Version to appear in PRD