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.

v4: 8 pages, no figures; Uses REVTeX 4.1; improved notation and additional comments/clarifications; updated references

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Cited by in corpus (8)

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• Gravitational waves in massive conformal gravity
• Linearized Field Equations and Extra Force in $f(R,{\mathbf{T}}^{(n)})$ Extended Gravity
• Second-order corrections to Starobinsky inflation
• Gravitational Waves Emission in Quadratic Gravity: longitudinal modes, angular momentum emission, and positivity of the radiated power
• Gauges for quadratic gravity: the extended transverse gauge and the energy-momentum tensor of the massive spin-2 field
• Quantum Geometrodynamics of Higher Derivative Theories with and without Conformal Symmetry