Asymptotic dynamics and charges for FLRW spacetimes

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.