I examine the standard formalism of calculating curvature perturbations in inflation at horizon crossing , and derive a general relation which must be satisfied for the horizon crossing formalism to be valid . This relation is satisfied for the usual cases of power-law and slow roll inflation . I then consider a model for which the relation is strongly violated , and the curvature perturbation evolves rapidly on superhorizon scales . This model has Hubble slow roll parameter \eta = 3 , but predicts a scale-invariant spectrum of density perturbations . I consider the case of hybrid inflation with large \eta , and show that such solutions do not solve the “ \eta problem ” in supergravity . These solutions correspond to field evolution which has not yet relaxed to the inflationary attractor solution , and may make possible new , more natural models on the string landscape .