Gravitational Waves in the Spectral Action of Noncommutative Geometry

Abstract

The spectral triple approach to noncommutative geometry allows one to develop the entire standard model (and supersymmetric extensions) of particle physics from a purely geometry stand point and thus treats both gravity and particle physics on the same footing. The bosonic sector of the theory contains a modification to Einstein-Hilbert gravity, involving a nonconformal coupling of curvature to the Higgs field and conformal Weyl term (in addition to a nondynamical topological term). In this paper we derive the weak field limit of this gravitational theory and show that the production and dynamics of gravitational waves are significantly altered. In particular, we show that the graviton contains a massive mode that alters the energy lost to gravitational radiation, in systems with evolving quadrupole moment. We explicitly calculate the general solution and apply it to systems with periodically varying quadrupole moments, focusing in particular on the the well know energy loss formula for circular binaries.

arXiv comment15 pages, 3 figures

References in corpus (10)

• The Confrontation between General Relativity and Experiment
• Gravity and the standard model with neutrino mixing
• The motion of point particles in curved spacetime
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Constraining the Noncommutative Spectral Action via Astrophysical Observations
• Cosmology and the Noncommutative approach to the Standard Model
• The Uncanny Precision of the Spectral Action
• Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action
• Natural inflation mechanism in asymptotic noncommutative geometry
• Scale Invariance in the Spectral Action

Cited by in corpus (27)

• Modified Gravity and Cosmology
• Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays
• Static Solutions for 4th order gravity
• Effective Gravitational Wave Stress-energy Tensor in Alternative Theories of Gravity
• Quantum gravity and gravitational-wave astronomy
• Astrophysical constraints on extended gravity models
• Constraints on NonCommutative Spectral Action from Gravity Probe B and Torsion Balance Experiments
• Noncommutative spectral geometry, algebra doubling and the seeds of quantization
• Spectral action with zeta function regularization
• Astrophysical Gravitational Waves in Conformal Gravity
• Spectral Regularisation: Induced Gravity and the Onset of Inflation
• Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology
• Restricting Fourth Order Gravity via Cosmology
• Probing Noncommutative Gravity with Gravitational Wave and Binary Pulsar Observations
• Coupling of gravity to matter, spectral action and cosmic topology
• Quantum Gravity and Cosmology: an intimate interplay
• Noncommutative spectral geometry, dissipation and the origin of quantization
• Doubling of the Algebra and Neutrino Mixing within Noncommutative Spectral Geometry
• Noncommutative Spectral Geometry: A Short Review
• Constraints on fourth order gravity from binary pulsar and gravitational waves
• Precession shift in curvature based Extended Theories of Gravity and Quintessence fields
• Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory
• Aspects of the Bosonic Spectral Action: Successes and Challenges
• Fractality in Cosmic Topology Models with Spectral Action Gravity
• Degravitation and the relaxed Einstein equations
• Unweaving the Fabric of the Universe: The Interplay between Mathematics and Physics
• Analytical constraints on gravitational models with a quadratic Weyl tensor