  We define the notion of energy, and compute its values, for gravitational
systems involving terms quadratic in curvature. While our construction
parallels that of ordinary Einstein gravity, there are significant differences
both conceptually and concretely. In particular, for D=4, all purely quadratic
models admit vacua of arbitrary constant curvature. Their energies, including
that of conformal (Weyl) gravity, necessarily vanish in asymptotically flat
spaces. Instead, they are proportional to that of the Abbott-Deser (AD) energy
expression in constant curvature backgrounds and therefore also proportional to
the mass parameter in the corresponding Schwarzschild-(Anti) de Sitter
geometries. Combined Einstein-quadratic curvature systems reflect the above
results: Absent a cosmological constant term, the only vacuum is flat space,
with the usual (ADM) energy and no explicit contributions from the quadratic
parts. If there is a Lambda term, then the vacuum is also unique with that
Lambda value, and the energy is just the sum of the separate contributions from
Einstein and quadratic parts to the AD expression . Finally, we discuss the
effects on energy definition of both higher curvature terms and higher
dimension.
