  This work analyzes bifurcation delay and front propagation in the
one-dimensional real Ginzburg-Landau equation (RGLE) with periodic boundary
conditions on monotonically growing or shrinking domains. First, we obtain
closed-form expressions for the delay of primary bifurcations on a growing
domain and show that the additional domain growth before the appearance of a
pattern is independent of the growth time scale. We also quantify primary
bifurcation delay on a shrinking domain; the time scale of domain compression
is reflected in the additional compression before the pattern decays. For
secondary bifurcations such as the Eckhaus instability, we obtain a lower bound
on the delay of phase slips due to a time-dependent domain. We also construct a
heuristic model to classify regimes with arrested phase slips, i.e. phase slips
that fail to develop. Then, we study how fronts are influenced by a
time-dependent domain. We derive expressions for the velocity and profile of
homogeneous fronts on a time-dependent domain. We also derive the natural
``asymptotic'' velocity and front profile and show that these deviate from
predictions based on the marginal stability criterion familiar from fixed
domain theory. This difference arises because the time-dependence of the domain
lifts the degeneracy of the spatial eigenvalues associated with speed selection
and represents a fundamental distinction from the fixed domain theory that we
verify using direct numerical simulations. The effect of a growing domain on
pattern-spreading and Eckhaus front velocities is inspected qualitatively and
found to be similar to that of homogeneous fronts. These more complex fronts
can also experience delayed onset. Lastly, we show that dilution -- an effect
present when the order parameter is conserved -- increases bifurcation delay
and amplifies changes in the homogeneous front velocity on time-dependent
domains.
