Quadratic gravity in first order formalism

Abstract

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 $\frac{1}{p^2}$. Calculations are somewhat involved when all monomials are considered, but we have intended to laid down the general case. The interaction between external sources is analyzed; this interaction is conveyed mainly by the three-index connection field. The theory as it stands, is in the 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 by quantum corrections.

50 pages, additions and new section. Version to be published in JCAP; Spotted errata corrected

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Cited by in corpus (9)

• Quadratic Gravity
• Dimensional Transmutation in Gravity and Cosmology
• Physical content of Quadratic Gravity
• Stability of non-degenerate Ricci-type Palatini theories
• Gravitational Coleman-Weinberg Mechanism
• Structural stability of spherical horizons
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Static and spherically symmetric solutions in a scenario with quadratic curvature contribution
• Divergences of the scalar sector of quadratic gravity