Celestial Ephemerides in an Expanding Universe
Sergei Kopeikin (University of Missouri, Columbia, USA)

TL;DR
This paper extends celestial dynamics theory to an expanding universe, deriving cosmological corrections to light propagation and proposing a method to measure the Hubble constant locally within the solar system.
Contribution
It formulates the Newtonian limit of Einstein's equations in an expanding universe and identifies missing cosmological terms in current light propagation models.
Findings
Equations of motion reduce to classical Newtonian form with conformal transformations.
Light propagation equations miss terms proportional to the Hubble constant.
Cosmological corrections enable local measurement of the Hubble constant.
Abstract
Post-Newtonian theory was instrumental in conducting the critical experimental tests of general relativity and in building the astronomical ephemerides of celestial bodies in the solar system with an unparalleled precision. The cornerstone of the theory is the postulate that the solar system is gravitationally isolated from the rest of the universe and the background spacetime is asymptotically flat. The present article extends this theoretical concept and formulates the principles of celestial dynamics of particles and light moving in gravitational field of a localized astronomical system embedded to the expanding Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. We formulate the precise mathematical concept of the Newtonian limit of Einstein's field equations in the conformally-flat FLRW spacetime and analyze the geodesic motion of massive particles and light in this limit. We…
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