  We consider the most general action for gravity which is quadratic in
curvature. In this case first order and second order formalisms are not
equivalent. This framework is a good candidate for a unitary and renormalizable
theory of the gravitational field; in particular, there are no propagators
falling down faster than $\tfrac{1}{p^2}$. The UV regime is in a conformal
invariant phase; only when Weyl invariance is broken through the coupling to
matter can an Einstein-Hilbert term (and its corresponding Planck mass scale)
be generated.
