The Pioneer anomalous acceleration: can we measure the cosmological constant at the scale of the solar system ?

Abstract

An anomalous constant acceleration of (8.7 \pm 1.3) x 10^-8 cm/s^2 directed toward the Sun has been discovered by Anderson et al. in the motion of the Pioneer 10/11 and Galileo spacecrafts. In parallel, the WMAP results have definitively established the existence of a cosmological constant Lambda=1/ L_U^2, and therefore of an invariant cosmic length-scale L_U=(2.72 \pm 0.10) Gpc. We show that the existence of this invariant scale definitively implements Mach's principle in Einstein's theory of general relativity. Then we demonstrate, in the framework of an exact cosmological solution of Einstein's field equations which is valid both locally and globally, that the definition of inertial systems ultimately depends on this length-scale. As a consequence, usual local coordinates are not inertial, so that the motion of a free body of speed v is expected to contain an additional constant acceleration a_P=v^2(\surd3 L_U), which is, using the WMAP five years results, (6.02 \pm 0.34) x 10^-8 cm/s^2 when v \approx c. Such an effect is too small to contribute significantly to the Pioneer acceleration (since v_Pioneer \approx 12 km/s << c), but could be possibly observed in a dedicated space mission.