  The separate-universe approach gives an intuitive way to understand the
evolution of cosmological perturbations in the long-wavelength limit. It uses
solutions of the spatially-homogeneous equations of motion to model the
evolution of the inhomogeneous universe on large scales. We show that the
separate-universe approach fails on a finite range of super-Hubble scales at a
sudden transition from slow roll to ultra-slow roll during inflation in the
very early universe. Such transitions are a feature of inflation models giving
a large enhancement in the primordial power spectrum on small scales, necessary
to produce primordial black holes after inflation. We show that the
separate-universe approach still works in a piece-wise fashion, before and
after the transition, but spatial gradients on finite scales require a
discontinuity in the homogeneous solution at the transition. We discuss the
implications for the $\delta N$ formalism and stochastic inflation, which
employ the separate-universe approximation.
