Energy of gravitational radiation in the de Sitter universe at I+ and at a horizon

Hamiltonian charges in the asymptotically de Sitter spacetimes

“…However, in section 4 authors noticed that this expression (in a radial Bondi gauge) has an ill-defined limit as Λ → 0 which led them to the change of considered boundary terms in Lagrangian 9 and thus different presymplectic form, potential and so also Hamiltonians and fluxes. Divergences in the limit Λ → 0 are in tension with [10,27] where this limit was explicitly checked (for the linearized gravity) but in an 'anti-radial' Bondi gauge. Thus it seems that this limit may depend non-trivially on the choice of gauge 10 and further investigations are needed.…”

“…Looking at (2.9), it is evident that this expression is Taylor expansion of (4.5) up to the quadratic terms. (The difference of signs is compensated by orientation of I) It was also shown in [27] that (4.25) reduces to the Trautman-Bondi mass loss law in the limit Λ → 0 which suggests that this is the correct formula for the energy density at null infinity.…”

“…In [27] flux of energy in the GR linearized around the de Sitter was calculated. To this end, we used a Killing vector ∂ u which generates translation from one null-cone to another in the Bondi coordinates in which the formula for the metric tensor reads…”

“…It is by no means in contradiction with the results of section 4.2 because that addition depends explicitly upon the distinguished foliation. 10 Since we consider transformations at I + , there is an additional subtlety, whether solutions considered in [37] and in [19,27] differ only by a gauge or rather an asymptotic symmetry.…”

“…The question of how to define the energy of gravitational waves (GW) in the presence of such Λ attracted JHEP05(2021)063 a lot of attention in the last few years (see e.g. [15,16,[16][17][18][19][20][21][22][23][24][25][26][27] for different definitions, proposal, arguments and calculations.) Since null infinity I is spacelike in asymptotically de Sitter spacetimes, this task is much harder -no natural timelike asymptotic symmetry is available.…”