  We study the particle spectrum and the unitarity of the generic n-dimensional
Weyl-invariant quadratic curvature gravity theories around their (anti-)de
Sitter [(A)dS] and flat vacua. Weyl symmetry is spontaneously broken in (A)dS
and radiatively broken at the loop level in flat space. Save the three
dimensional theory (which is the Weyl-invariant extension of the new massive
gravity), the graviton remains massless and the unitarity requires that the
only viable Weyl-invariant quadratic theory is the Weyl-invariant extension of
the Einstein-Gauss-Bonnet theory. The Weyl gauge field on the other hand
becomes massive. Symmetry breaking scale fixes all the dimensionful parameters
in the theory.
