  We study the growth of superhorizon modes in the curvature perturbation
during an ultra-slow-roll or a large-$\eta$ phase in single-field inflation. In
a simple toy model, we derive the two-point correlation function of the
curvature perturbation and show that the requirement for causality restricts
the growth rate and hence puts a lower limit on the value of $\eta$. The toy
model is then realized by considering an inflation potential with an inflection
point. Our study is useful to assessing the growth of the curvature
perturbation that seeds the formation of primordial black holes.
