Cosmic parallax as a probe of late time anisotropic expansion

Cosmic parallax is the change of angular separation between a pair of sources at cosmological distances induced by an anisotropic expansion. An accurate astrometric experiment like Gaia could observe or put constraints on cosmic parallax. Examples of anisotropic cosmological models are Lemaitre-TolmanBondi void models for off-center observers (introduced to explain the observed acceleration without the need for dark energy) and Bianchi metrics. If dark energy has an anisotropic equation of state, as suggested recently, then a substantial anisotropy could arise at z less than or similar to 1 and escape the stringent constraints from the cosmic microwave background. In this paper we show that such models could be constrained by the Gaia satellite or by an upgraded future mission.