  We investigate by rheology and light scattering the influence of the elastic
modulus, $G_0$, on the slow dynamics and the aging of a soft glass. We show
that the slow dynamics and the aging can be entirely described by the evolution
of an effective viscosity, $\eta_{eff}$, defined as the characteristic time
measured in a stress relaxation experiment times $G_0$. At all time,
$\eta_{eff}$ is found to be independent of $G_0$, of elastic perturbations, and
of the rate at which the sample is quenched in the glassy phase. We propose a
simple model that links $\eta_{eff}$ to the internal stress built up at the
fluid-to-solid transition.
