Solar system tests of the cosmological constant

TL;DR

This paper examines how the cosmological constant affects planetary and stellar motions, deriving observational constraints from orbital data, and discusses implications for dark matter and alternative gravity theories.

Contribution

It provides a detailed analysis of the influence of the cosmological constant on gravitational dynamics within the solar system and binary systems, offering new constraints and discussing alternative gravity models.

Findings

Earth and Mars data constrain Λ to about 10^{-36} km^{-2}

Properly accounting for gravito-magnetic effects can improve constraints

Dark matter and modified gravity models are also discussed

Abstract

We discuss the influence of the cosmological constant $\Lambda$ on the gravitational equations of motion of bodies with arbitrary masses and eventually solve the two-body problem. Observational constraints are derived from measurements of the periastron advance in stellar systems, in particular binary pulsars and the solar system. For the latter we consider also the change in the mean motion due to $\Lambda$. Up to now, Earth and Mars data give the best constraint, $\Lambda \sim 10^{-36} \mathrm{km}^{-2}$. If properly accounting for the gravito-magnetic effect, this upper limit on $\Lambda$ could greatly improve in the near future thanks to new data from planned or already operating space-missions. Dark matter or modifications of the Newtonian inverse-square law in the solar system are discussed as well. Variations in the $1/r^2$ behavior are considered in the form of either a possible Yukawa-like interaction or a modification of gravity of MOND type.