Exact Relation between Einstein and Quadratic Quantum Gravity

TL;DR

This paper demonstrates an exact equivalence between the path integral formulations of quadratic and Einstein gravity, revealing complex interactions and instabilities, with implications for understanding quantum gravity.

Contribution

It establishes an exact relation between quadratic and Einstein gravity path integrals, including the role of massive fields and their interactions.

Findings

Path integral of quadratic gravity equals that of Einstein gravity with additional fields.

Both massive excitations are unstable.

Cosmological constants can differ significantly between formulations.

Abstract

We show the exact equality of the path integral of the general renormalizable fourth order gravitational action to the path integral of the Einstein action coupled to a massive spin-0 field and a massive spin-2 ghost-like field with non-polynomial interactions. The metric in the Einstein version is a highly nonlinear function of the metric in the quadratic version. Both massive excitations are unstable. The respective cosmological constant terms in the two versions can be very different. Some implications are briefly discussed.