Asymptotic dynamics and charges for FLRW spacetimes

TL;DR

This paper explores the asymptotic structure of FLRW spacetimes at future null infinity, revealing an enlarged symmetry algebra similar to Weyl-BMS, and analyzes the associated charges and dynamics constrained by the energy-momentum tensor.

Contribution

It extends the Weyl-BMS algebra to FLRW spacetimes by relaxing boundary conditions and studies the resulting charges and their evolution in a cosmological context.

Findings

The asymptotic algebra matches the Weyl-BMS algebra for flat spacetimes.

The dynamics are fully determined by the source's energy-momentum tensor.

A new contribution from Hubble flow affects the charge evolution.

Abstract

We investigate the asymptotia of decelerating and spatially flat FLRW spacetimes at future null infinity. We find that the asymptotic algebra of diffeomorphisms can be enlarged to the recently discovered Weyl-BMS algebra for asymptotically flat spacetimes by relaxing the boundary conditions. This algebra remains undeformed in the cosmological setting contrary to previous extensions of the BMS algebra. We then study the equations of motion for asymptotically FLRW spacetimes with finite fluxes and show that the dynamics is fully constrained by the energy-momentum tensor of the source. Finally, we propose an expression for the charges that are associated with the cosmological supertranslations and whose evolution equation features a novel contribution arising from the Hubble-Lema\^itre flow.