  We use large-scale Monte Carlo simulations to obtain comprehensive results
for domain growth and aging in the random field XY model in dimensions $d=2,3$.
After a deep quench from the paramagnetic phase, the system orders locally via
annihilation of topological defects, i.e., vortices and anti-vortices. The
evolution morphology of the system is characterized by the correlation function
and the structure factor of the magnetization field. We find that these
quantities obey dynamical scaling, and their scaling function is independent of
the disorder strength $\Delta$. However, the scaling form of the
autocorrelation function is found to be dependent on $\Delta$, i.e.,
superuniversality is violated. The large-$t$ behavior of the autocorrelation
function is explored by studying aging and autocorrelation exponents. We also
investigate the characteristic growth law $L(t,\Delta)$ in $d=2,3$, which shows
an asymptotic logarithmic behavior: $L(t,\Delta) \sim \Delta^{-\varphi} (\ln
t)^{1/\psi}$, with exponents $\varphi, \psi > 0$.
