  We investigate the effects of fluctuations on the dynamics of an isolated
quantum system represented by a $\phi^4$ field theory with $O(N)$ symmetry
after a quench in $d>2$ spatial dimensions. A perturbative
renormalization-group approach involving a dimensional expansion in
$\epsilon=4-d$ is employed in order to study the evolution within a prethermal
regime controlled by elastic dephasing. In particular, we focus on a quench
from a disordered initial state to the critical point, which introduces an
effective temporal boundary in the evolution. At this boundary, the relevant
fields acquire an anomalous scaling dimension, while the evolution of both the
order parameter and its correlation and response functions display universal
aging. Since the relevant excitations propagate ballistically, a light cone in
real space emerges. At longer times, the onset of inelastic scattering appears
as secularly growing self-generated dissipation in the effective Keldysh field
theory, with the strength of the dissipative vertices providing an estimate for
the time needed to leave the prethermal regime.
