  Motivated by the mean field prediction of a Gardner phase transition between
a "normal glass" and a "marginally stable glass", we investigate the
off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used
as a model for colloidal or granular glasses. Deep inside the glass phase, we
find that a sharp crossover pressure $P_{\rm G}$ separates two distinct
dynamical regimes. For pressure $P < P_{\rm G}$, the glass behaves as a normal
solid, displaying fast dynamics that quickly equilibrates within the glass free
energy basin. For $P>P_{\rm G}$, instead, the dynamics becomes strongly
anomalous, displaying very large equilibration time scales, aging, and a
constantly increasing dynamical susceptibility. The crossover at $P_{\rm G}$ is
strongly reminiscent of the one observed in three-dimensional spin-glasses in
an external field, suggesting that the two systems could be in the same
universality class, consistently with theoretical expectations.
