Solar and stellar system tests of the cosmological constant

Abstract

Some tests of gravity theories -periastron shift, geodetic precession, change in mean motion and gravitational redshift -are applied in solar and stellar systems to constrain the cosmological constant. We thus consider a length scale range from ∼ 10 8 to ∼ 10 15 km. Best bounds from the solar system come from perihelion advance and change in mean motion of Earth and Mars, Λ < ∼ 10 −36 km −2 . Such a limit falls very short to estimates from observational cosmology analyses but a future experiment performing radio ranging observations of outer planets could improve it by four orders of magnitude. Beyond the solar system, together with future measurements of periastron advance in wide binary pulsars, gravitational redshift of white dwarfs can provide bounds competitive with Mars data.PACS numbers: 04.80. Cc,95.10.Ce,95.30.Sf,95.36.+x,

Evolution of gravitational orbits in the expanding universe

“…In a de Sitter model (Ω M0 = 0), thenR/R = c 2 Λ/3, and we retrieve the well known result for extra-precession due to a cosmological constant as usually obtained in the framework of the Schwarzschild-de Sitter metric [11,19]. The rate of precession predicted for the Earth is ∼ −5 × 10 −16 q 0 h 2 arcsec per year, ∼ 10 −16 arcsec per year in our reference ΛCDM model with h = 0.7.…”

“…The statistical error on the mean motion for each major planet can be evaluated from the uncertainty on the semi-major axis, δn = −(3/2)nδa/a, and can then be translated into an uncertainty on the effective acceleration. When attempting to detect exotic physics in the Solar system with today data on changes in the mean motion, best bounds come from Earth and Mars [11,13]. In our reference ΛCDM model, the today deceleration parameter is q 0 = −0.55.…”

“…We assume that the time dependence of the perturbations in Eqs. (10,11) is due to the time variation of the perturbing function. Substituting in Eqs.…”

“…In a series of previous papers, we discussed the effect on a local bound system of the cosmological constant [11,12] and of diffuse dark matter [13]. In this paper we investigate the evolution of a planet orbit around a massive star embedded in an homogeneous and isotropic universe.…”

Contribution of the cosmological constant to the relativistic bending of light revisited

“…The argument for the non-influence of Λ was apparently first made in [9] and has been re-made and reaffirmed by other authors, see for example [10,11,12,13,14]. The common basis of their arguments is that, in the Schwarzschild-de Sitter metric (first derived by Kottler [15]), which applies when Λ is included, Λ nevertheless drops out of the exact r, φ differential equation for a light path (null geodesic).…”