Quadratic gravity in first order formalism

Understand

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 $\tfrac{1}{p^2}$.
• Calculations are somewhat involved when all monomials are considered, but we have intended to laid down the general case.