Gravitational Energy in Quadratic-Curvature Gravities

We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Λ, and E is the “cosmological” Abbott-Deser (AD) expression; instead, E always vanishes in flat, Λ=0, background. For combined Einstein-quadratic curvature systems without explicit Λ-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Λ-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.