A positive energy theorem for asymptotically de Sitter spacetimes

Abstract

We construct a set of conserved charges for asymptotically de Sitter spacetimes that correspond to asymptotic conformal isometries. The charges are given by boundary integrals at spatial infinity in the flat cosmological slicing of de Sitter. Using a spinor construction, we show that the charge associated with conformal time translations is necessarily positive and hence may provide a useful definition of energy for these spacetimes. A similar spinor construction shows that the charge associated with the time translation Killing vector of de Sitter in static coordinates has both positive and negative definite contributions. For Schwarzschild–de Sitter the conformal energy we define is given by the mass parameter times the cosmological scale factor. The time dependence of the charge is a consequence of a nonzero flux of the corresponding conserved current at spatial infinity. For small perturbations of de Sitter, the charge is given by the total comoving mass density.