A non-perturbative and background-independent formulation of quadratic gravity

Abstract

A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to obtain, as required by consistency, a well-defined Euclidean path integral. The theory is unitary: all probabilities are non negative and they sum up to one. We obtain path-integral expressions for the transition amplitudes, Green's functions and generic matrix elements of time-ordered products of the metric. As a byproduct, similar results are also obtained for a scalar-field four-derivative interacting model. In this way, among other things, previous perturbative and background-dependent calculations are justified. The (quantum) quadratic gravity effective action, whose field equations determine the vacuum expectation value of the metric in the presence of a generic energy-momentum tensor, is constructed. The classical limit of the effective action turns out to be equivalent to the starting classical action of quadratic gravity, whose runaway rates were previously shown to be slow enough to be compatible with observations. Finally, the constructed non-perturbative and background-independent quantum quadratic gravity is applied to quantum cosmology to obtain a path-integral expression for the wave function of the universe, which satisfies a sort of Wheeler-DeWitt equation. This application allows us to understand at the quantum level why our universe is nearly homogeneous and isotropic.