Asymptotics with a positive cosmological constant. II. Linear fields on de Sitter spacetime

Linearized gravitational waves in de Sitter spacetime 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 I is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from Diff(I) 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 I⁺. (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. Finally, (iv) we demonstrate that the flux formulas reduce to the familiar ones in Minkowski spacetime in spite of the fact that the limit Λ→0 is discontinuous (since, in particular, I changes its spacelike character to null in the limit).