Gravitational Effective Action at Second Order in Curvature and Gravitational Waves

TL;DR

This paper analyzes the quantum gravity effective action at second order in curvature, revealing additional degrees of freedom and discussing their implications for gravitational waves and Newtonian potential deviations.

Contribution

It demonstrates the presence of a massive spin-2 ghost and scalar in the effective theory and explores how to measure the parameters of the local terms through gravitational wave and pendulum experiments.

Findings

Existence of a massive spin-2 ghost and scalar in the effective theory.

Impossible to eliminate the ghost through parameter fine-tuning due to non-local terms.

Potential to measure local effective action parameters via gravitational wave and Newtonian potential experiments.

Abstract

We consider the full effective theory for quantum gravity at second order in curvature including non-local terms. We show that the theory contains two new degrees of freedom beyond the massless graviton: namely a massive spin-2 ghost and a massive scalar field. Furthermore, we show that it is impossible to fine-tune the parameters of the effective action to eliminate completely the classical spin-2 ghost because of the non-local terms in the effective action. Being a classical field, it is not clear anyway that this ghost is problematic. It simply implies a repulsive contribution to Newton's potential. We then consider how to extract the parameters of the effective action and show that it is possible to measure, at least in principle, the parameters of the local terms independently of each other using a combination of observations of gravitational waves and measurements performed by pendulum type experiments searching for deviations of Newton's potential.