  We propose a first-principles theoretical approach for the description of the
aging of the linear viscoelastic properties of a colloidal liquid after a
sudden quench into a dynamically arrested (glass or gel) state. Specifically,
we couple a general expression for the time-evolving shear-stress relaxation
function $\eta(\tau;t)$ (whose $\tau$-integral is the instantaneous viscosity
$\eta(t)$), written in terms of the non-equilibrium structure factor $S(k;t)$
and intermediate scattering function $F(k,\tau;t)$, with the equations that
determine $S(k;t)$ and $F(k,\tau;t)$, provided by the non-equilibrium
self-consistent generalized Langevin equation (NE-SCGLE) theory. In this
manner, we obtain a closed theoretical scheme that directly connects
inter-particle forces with experimentally accessible rheological properties of
non-equilibrium amorphous states of matter. The predictive capability of the
resulting theoretical formalism is illustrated here with its concrete
application to the Weeks-Chandler-Andersen (WCA) model of a soft-sphere fluid.
