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 $\Lambda \to 0$ is discontinuous (since, in particular, $\scri$ changes its space-like character to null in the limit).