The $SO(1,4)$ flux-balance laws of de Sitter at quadrupolar order

TL;DR

This paper derives flux-balance laws for quadrupolar perturbations in de Sitter spacetime, connecting symmetry fluxes to source moments and comparing energy flux proposals, with flat limit consistency.

Contribution

It provides explicit flux-balance laws for de Sitter symmetries at quadrupolar order, including two formulations of dilatation flux and their relation to energy flux.

Findings

Two distinct dilatation flux formulations are presented.

Flux-balance laws recover Poincaré laws in the flat limit.

The paper clarifies the negative definite energy flux proposals.

Abstract

The linear solution for quadrupolar perturbations around de Sitter spacetime was recently constructed. In this paper, we provide the flux-balance laws for each background symmetry (dilatations, rotations, spatial translations and cosmological boosts) in terms of source moments at quadrupolar order. We write the dilatation flux-balance law in two distinct ways, which allows to contrast two distinct proposals for the negative definite energy flux. The standard Poincar\'e flux balance laws at future null infinity are recovered in the flat limit of the $SO(1,4)$ flux-balance laws.