Gravitational Waves and Perspectives for Quantum Gravity

TL;DR

This paper investigates the impact of higher derivative terms and massive ghosts in quantum gravity, proposing a new approach to address stability issues by analyzing gravitational wave dynamics on classical backgrounds.

Contribution

It introduces a novel, simpler method to handle ghost-induced instabilities in quantum gravity by examining gravitational wave behavior on classical solutions.

Findings

Massive ghosts cause instability only as physical particles.

No instabilities occur if initial perturbation frequency is below ghost mass.

Proposes a new approach to manage higher derivative ghost issues.

Abstract

Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector. The same situation holds in the quantum theory of metric. At the same time, including the fourth derivative terms means the presence of massive ghosts, which are gauge-independent massive states with negative kinetic energy. At both classical and quantum level such ghosts violate stability and hence the theory becomes inconsistent. Several approaches to solve this contradiction were invented and we are proposing one more, which looks simpler than those what were considered before. We explore the dynamics of the gravitational waves on the background of classical solutions and give certain arguments that massive ghosts produce instability only when they are present as physical particles. At least on the cosmological background one can observe that if the initial frequency of the metric perturbations is much smaller than the mass of the ghost, no instabilities are present.