Note on the perihelion/periastron advance due to cosmological constant

Abstract

We will comment on the perihelion/periastron advance of celestial bodies due to the cosmological constant $\Lambda$. It is well known that the cosmological constant $\Lambda$ causes the perihelion/periastron shift; however, there seems to still exist a discrepancy among the various derived precession formulae. We will point out that the expression $\Delta {\omega }_{\Lambda }=(\pi c^2\Lambda a^3/(GM))\sqrt{1-e^2}$ is the general formula for any orbital eccentricity $e$ and the expression $\Delta {\omega }_{\Lambda }=(\pi c^2\Lambda a^3/(GM))(1-e^2{)}^3$ comes from the nearly circular ($e\ll 1$) approximation.

8 pages, 1 figure, accepted for publication in International Journal of Theoretical Physics

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• Anti-de Sitter neutron stars in the theory of gravity with nonminimal derivative coupling
• Local coordinates and motion of a test particle in the McVittie spacetime
• Orbital precession and other properties of two-body motion in the presence of dark energy
• Deflection and gravitational lensing of null and timelike signals in general asymptotically (anti-)de Sitter spacetimes