Astrophysical Gravitational Waves in Conformal Gravity

Abstract

We investigate the gravitational radiation from binary systems in conformal gravity (CG) and massive conformal gravity (MCG). CG might explain observed galaxy rotation curves without dark matter, and both models are of interest in the context of quantum gravity. Here we show that gravitational radiation emitted by compact binaries allows us to strongly constrain both models. We work in Weyl gauge, which fixes the rescaling invariance of the models, and derive the linearized fourth-order equation of motion for the metric, which describes massless and massive modes of propagation. In the limit of a large graviton mass, MCG reduces to general relativity (GR), whereas CG does not. Coordinates are fixed by Teyssandier gauge to show that for a conserved energy-momentum tensor the gravitational radiation is due to the time-dependent quadrupole moment of a non-relativistic source and we derive the gravitational energy-momentum tensor for both models. We apply our findings to the case of close binaries on circular orbits, which have been used to indirectly infer the existence of gravitational radiation prior to the direct observation of gravitational waves. As an example, we analyze the binary system PSR J1012+5307, chosen for its small eccentricity. When fixing the graviton mass in CG such that observed galaxy rotation curves could be explained without dark matter, the gravitational radiation of a binary system is much smaller than in GR. The same holds for MCG for small masses of the graviton. Thus gravitational radiation cannot explain the orbital decay of binary systems and replace dark matter simultaneously. We also analyse MCG for large graviton masses and conclude that MCG can describe the orbital periods of compact binaries in agreement with data, as it reduces to GR in that limit.

v2: 21 pages, no figures; Uses REVTeX 4.1; added a comment and references in section 1; corrected sign in eqn. (3)

References in corpus (25)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• The Confrontation between General Relativity and Experiment
• Multi-messenger Observations of a Binary Neutron Star Merger
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Making Sense of Non-Hermitian Hamiltonians
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence
• Swope Supernova Survey 2017a (SSS17a), the Optical Counterpart to a Gravitational Wave Source
• Tests of general relativity from timing the double pulsar
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Avoiding Dark Energy with 1/R Modifications of Gravity
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Fourth order Weyl gravity
• From conformal to Einstein Gravity
• On the Quantisation of Complex Higher Derivative Theories and Avoiding the Ostrogradsky Ghost
• Constraining the Noncommutative Spectral Action via Astrophysical Observations
• Conformal Weyl gravity and perihelion precession
• Gravitational Waves in the Spectral Action of Noncommutative Geometry
• Schwarzschild limit of conformal gravity in the presence of macroscopic scalar fields
• Giving up the ghost
• Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime
• Gauge Choice in Conformal Gravity

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• Probing alternative cosmologies through the inverse distance ladder
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• Comment on "Astrophysical gravitational waves in conformal gravity"
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