Post-Newtonian celestial mechanics in scalar-tensor cosmology

Abstract

Applying the recently developed dynamical perturbation formalism on cosmological background to scalar-tensor theory, we provide a solid theoretical basis and a rigorous justification for phenomenological models of orbital dynamics that are currently used to interpret experimental measurements of the time-dependent gravitational constant. We derive the field equations for the scalar-tensor perturbations and study their gauge freedom associated with the cosmological expansion. We find a new gauge eliminating a prohibitive number of gauge modes in the field equations and significantly simplifying post-Newtonian equations of motion for localized astronomical systems in the universe with time-dependent gravitational constant. We identify several new post-Newtonian terms and calculate their effect on secular cosmological evolution of the osculating orbital elements.

7 pages, no figures; supplemental materials added: "Derivation of the wave equations for perturbations", 27 pages, no figures

References in corpus (6)

• The Confrontation between General Relativity and Experiment
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• Celestial Ephemerides in an Expanding Universe
• Post-Newtonian Celestial Dynamics in Cosmology: Field Equations
• Planetary Orbital Equations in Externally-Perturbed Systems: Position and Velocity-Dependent Forces
• Dynamic Field Theory and Equations of Motion in Cosmology

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• On the foundations of general relativistic celestial mechanics
• Local coordinates and motion of a test particle in the McVittie spacetime
• Covariant Equations of Motion Beyond the Spin-Dipole Particle Approximation
• Post-Newtonian Lagrangian of an N-body System with Arbitrary Mass and Spin Multipoles
• The cosmological constant emerging from a symmetry invariant