  In polymers melts and supercooled liquids, the glassy dynamics is
characterized by the rattling of monomers or particles in the cage formed by
their neighbors. Recently, a direct correlation in such systems, described by a
universal scaling form, has been established between the rattling amplitude and
the structural relaxation time. In this paper we analyze the glassy dynamics
emerging from the formation of a persistent network in a model colloidal gel at
very low density. The structural relaxation time of the gel network is compared
with the mean squared displacement at short times, corresponding to the
localization length associated to the presence of energetic bonds.
Interestingly, we find that the same type of scaling as for the dense glassy
systems holds. Our findings well elucidate the strong coupling between the
cooperative rearrangements of the gel network and the single particle
localization in the structure. Our results further indicate that the scaling
captures indeed fundamental physical elements of glassy dynamics.
