  We propose a new single field inflation model in which the usual slow-roll
inflation is joined to a new period of slow-climb and slow-roll inflation
through a short intermediate non-inflationary phase. We then show that
primordial curvature perturbations can be enhanced at small scales, a sizable
amount of primordial black holes (PBHs) can be produced which make up most of
dark matter, the gravitational waves (GWs) induced by scalar metric
perturbations that accompany with the formation of PBHs can be detectable by
future GW experiments, and last but not least, our model is compatible with the
latest cosmic microwave background observations. Remarkably, the GW spectrum
displays a unique oscillating character in the ultraviolet regions which
originates from the short non-inflationary phase. A detection of such
oscillations in the GW spectrum may suggest the existence of such a
non-inflationary phase in the whole inflation, thus providing us a chance to
reveal an interesting period in the evolution of the early Universe and
distinguish our model from others.
