Post-Newtonian celestial mechanics in scalar-tensor cosmology

TL;DR

This paper develops a rigorous theoretical framework for scalar-tensor cosmology, deriving simplified post-Newtonian equations of motion that account for a time-dependent gravitational constant and analyzing their impact on orbital dynamics.

Contribution

It introduces a new gauge choice that simplifies post-Newtonian equations in scalar-tensor cosmology and derives new terms affecting orbital evolution.

Findings

New gauge reduces gauge modes in field equations

Derived new post-Newtonian terms affecting orbital elements

Quantified effects on secular cosmological evolution

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.