  We demonstrate non-equilibrium scaling laws for the aging dynamics in glass
formers that emerge from combining a recent application of Onsager's theory of
irreversible processes with the equilibrium scaling laws of glassy dynamics.
Different scaling regimes are predicted for the evolution of the system's
structural relaxation time $\tau$ with age (waiting time $t_w$), depending on
the depth of the quench from the liquid into the glass: \emph{simple aging}
($\tau\sim t_w$) applies for quenches close to the critical point of
mode-coupling theory (MCT) and implies \emph{sub-aging} ($\tau\approx\
t_w^\delta$ with $\delta<1$) as a broad cross-over for quenches to
nearly-arrested equilibrium states; \emph{hyper-aging} (or \emph{super-aging},
$\tau\sim t_w^{\delta'}$ with $\delta'>1$) emerges for quenches deep into the
glass. The latter is cut off by non-mean-field fluctuations that we account for
within a recent extension of MCT, the stochastic $\beta$-relaxation theory
(SBR). We exemplify the scaling laws by a schematic model that allows to
quantitatively fit recent simulation results for density-quenched
hard-sphere-like particles.

Soft Condensed Matter