Space-dependent step features: Transient breakdown of slow-roll, homogeneity, and isotropy during inflation

A step feature in the inflaton potential can model a transient breakdown of slow-roll inflation. Here we generalize the step feature to include space-dependence, allowing it also to model a breakdown of homogeneity and isotropy. The space-dependent inflaton potential generates a classical curvature perturbation mode characterized by the wave number of the step inhomogeneity. For inhomogeneities small compared with the horizon at the step, space-dependence has a small effect on the curvature perturbation. Therefore, the smoothly oscillating quantum power spectrum predicted by the homogeneous step is robust with respect to subhorizon space-dependence. For inhomogeneities equal to or greater than the horizon at the step, the space-dependent classical mode can dominate, producing a curvature perturbation in which modes of wave number determined by the step inhomogeneity are superimposed on the oscillating power spectrum. Generation of a space-dependent step feature may therefore provide a mechanism to introduce primordial anisotropy into the curvature perturbation. Space-dependence also modifies the quantum fluctuations, in particular, via resonancelike features coming from mode coupling to amplified superhorizon modes. However, these effects are small relative to the classical modes.