Gravitational Waves and Degrees of Freedom in Higher Derivative 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.