Gravitational Waves and Degrees of Freedom in Higher Derivative Gravity

TL;DR

This paper analyzes the degrees of freedom in higher derivative gravity models, revealing how additional modes behave and contribute to gravitational radiation, with implications for quantum gravity theories.

Contribution

It provides a linearized analysis of higher derivative gravity in arbitrary dimensions, showing the dynamical gauge conditions and mode excitations, especially in quadratic gravity in four dimensions.

Findings

Harmonic gauge condition is dynamically induced.

Only transverse modes are excited by matter sources.

Quadrupole moment is the sole contributor to gravitational radiation in 4D quadratic gravity.

Abstract

We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable. First, we linearize the theory for a flat background metric in Teyssandier gauge for an arbitrary number of spacetime dimensions $D$. The higher-order derivative field equations for the metric perturbation can be decomposed into tensorial and scalar field equations resembling massless and massive wave equations. For the massive tensor field in $D$-dimensions we demonstrate that the harmonic gauge condition is induced dynamically and only the transverse modes are excited in the presence of a matter source. For the special case of quadratic gravity in four-dimensional spacetime, we show that only the quadrupole moment contributes to the gravitational radiation from an idealized binary system.