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

TL;DR

This paper analyzes linear gravitational waves in de Sitter space-time to guide the development of a theory of gravitational radiation with a positive cosmological constant, highlighting key geometric and energetic properties.

Contribution

It provides explicit expressions for energy-momentum fluxes, challenges the assumption of conformal flatness of infinity, and explores the behavior of gravitational waves as the cosmological constant approaches zero.

Findings

Conformal flatness of infinity is physically unreasonable.

Energy fluxes are expressed in terms of fields at infinity.

Gravitational waves from realistic sources carry positive energy.

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).