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.

Gravitational waves in massive conformal gravity

“…which reduce the independent components of a µν to just two. Thus, we conclude that the MCG plane gravitational wave (33) has seven propagating degrees of freedom, represented by the two independent components of a µν and the five independent components of b µν , which is consistent with recent results obtained in the literature [8,9].…”

Gravitational waves in massive conformal gravity

“…which reduce the independent components of a μν to just two. Thus, we conclude that the MCG plane gravitational wave (33) has seven propagating degrees of freedom, represented by the two independent components of a μν and the five independent components of b μν , which is consistent with recent results obtained in the literature [8,10].…”

Probing quadratic gravity with binary inspirals

“…This comes from the requirement that the frequency of the waves arriving at the detector, given approximately by an inspiral angular velocity ω ≈ v/r , must exceed the mass, ω > m φ,π and this requirement is in contradiction with the constraints m φ,π r > 1, since v < 1 during the inspiral phase. Therefore we do not expect massive waves to be produced during the inspiral phase (see also [29]). We would like to stress that these conclusions are conservative and are purely based on the validity of quadratic gravity as an effective field theory.…”