The influence of gravity on the long-time behavior of the mean squared displacement in glasses of polydisperse colloidal hard spheres was studied by means of real-space fluorescent recovery after photobleaching. We present, for the first time, a significant influence of gravity on the mean squared displacements of the particles. In particular, we observe that systems which are glasses under gravity (with a gravitational length on the order of tens of micrometers) show anomalous diffusion over several decades in time if the gravitational length is increased by an order of magnitude. No influence of gravity was observed in systems below the glass transition density. We show that this behavior is caused by gravity dramatically accelerating aging in colloidal hard sphere glasses. This behavior explains the observation that colloidal hard sphere systems which are a glass on Earth rapidly crystallize in space. DOI: 10.1103/PhysRevLett.93.035701 PACS numbers: 64.70.Pf, 05.40.Jc, 82.70.Dd Hard spheres for which the potential energy is infinite on overlap and (in the absence of fields) zero otherwise freeze upon increasing number density from a fluid into a crystal at a volume fraction, , of 0.494 [1,2]. In between 0:494 and 0.545, fluid and crystal coexist [3], while, at even higher volume fractions, a single phase (fcc [4]) crystal is thermodynamically stable up to the close packed density corresponding to =3 2 p 0:74. Colloids may behave as hard spheres [6]. Besides the thermodynamic freezing transition referred to above, colloidal hard spheres can be brought in a (long-lasting) metastable fluid state by rapid quenching using centrifugation [6]. In the resulting colloidal glass, large-scale particle diffusion and crystallization by homogeneous nucleation stop, implying that crystal nucleation proceeds by large-scale particle diffusion [6,7]. The glass state is reached at a surprisingly small number density of the hard spheres: 0:57-0:58, a significantly smaller density than where (monodisperse) hard spheres are jammed at random close packing with 0:64 [8]. It is widely believed that the glass transition of hard spheres corresponds to permanent caging of the particles by their neighbors [7,9]. However, recent computer simulations [10] and experiments under microgravity [11] pose serious doubts on the very existence of a glass transition at < 0:64 of monodisperse hard spheres in the absence of a gravity field. These studies show that monodisperse [10] but also (about 5%) polydisperse [11] hard spheres crystallize in the absence of gravity up to volume fractions close to 0.64. In the last study, a system that is a glass on Earth rapidly crystallizes in space after homogenization by mixing.While microscopic particle movements do not seem to be affected by details of the particle size distribution [12], as far as we are aware, no quantitative studies of the influence of gravity on dynamics in concentrated colloidal suspensions have been reported. In this work we address the question as to what the influence of gravity ...