 Growing curvature perturbation in ultra-slow-roll inflation

In ultra-slow-roll inflation, $z=a\sqrt{2ϵ}\propto a^{-2}\propto {\eta }^2$. The comoving curvature mode equation isand its Bunch-Davies mode is proportional to $(1+ik\eta )e^{-ik\eta }/{\eta }^3$. Unlike ordinary slow roll, the superhorizon curvature perturbation grows as $a^3$.