Solar system tests of the cosmological constant

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.