Asymptotic Symmetries and Charges in De Sitter Space

TL;DR

The paper defines the asymptotic symmetry group for asymptotically de Sitter spacetimes at future null infinity as all three-dimensional diffeomorphisms on I^+. It constructs finite charges for these symmetries using a Brown–York stress tensor with counterterms and derives a flux-driven conservation law that ties charge evolution to radiation through I^+. Through a covariant phase space analysis and Wald–Zoupas corrections, the charges are shown to be integrable and equivalent to Brown–York charges, clarifying how gravitational radiation affects the asymptotic charges. These results establish a rigorous framework for handling asymptotic charges in de Sitter space, with potential implications for de Sitter holography and the physics of an expanding universe.

Abstract

The asymptotic symmetry group (ASG) at future null infinity (I^+) of four-dimensional de Sitter spacetimes is defined and shown to be given by the group of three-dimensional diffeomorphisms acting on I^+. Finite charges are constructed for each choice of ASG generator together with a two-surface on I^+. A conservation equation is derived relating the evolution of the charges with the radiation flux through I^+.

Figures (1)

• Figure 1: Consider two spacelike slices $\Sigma_1$ and $\Sigma_2$ ending on $\partial \Sigma_1$ and $\partial \Sigma_2$. The difference between the Brown-York charge $\Delta Q_{BY}$ is given by the integral over the radiation flux ${F}_\xi$ in the 3-volume ($\mathcal{B}_{12}$ in ${\cal I}^+$) bounded by $\partial \Sigma_1$ and $\partial \Sigma_2$. Here, the Penrose diagram depicts a spacetime which tends to de Sitter space in the far future. The spacelike jagged line represents the far past which could for example be the big bang.