A Positive Energy Theorem for Asymptotically deSitter Spacetimes

TL;DR

This paper introduces a positive energy theorem for asymptotically deSitter spacetimes, defining conserved charges via boundary integrals and spinor methods, ensuring positivity for conformal energy in these cosmological models.

Contribution

It constructs conserved charges for asymptotically deSitter spacetimes using boundary integrals and spinor techniques, establishing a positive energy theorem in this context.

Findings

Conserved charges correspond to asymptotic conformal isometries.

The conformal energy is positive and related to the mass parameter.

Time dependence arises from flux at spatial infinity.

Abstract

We construct a set of conserved charges for asymptotically deSitter spacetimes that correspond to asymptotic conformal isometries. The charges are given by boundary integrals at spatial infinity in the flat cosmological slicing of deSitter. Using a spinor construction, we show that the charge associated with conformal time translations is necessarilly 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 deSitter in static coordinates has both positive and negative definite contributions. For Schwarzshild-deSitter 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 non-zero flux of the corresponding conserved current at spatial infinity. For small perturbations of deSitter, the charge is given by the total comoving mass density.