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We consider an inflationary kinetic function with an integrable pole that istraversed during inflation. This scenario leads to enhanced spectra ofprimordial scalar inhomogeneities with detectable signals: formation ofprimordial black holes (that could explain Dark Matter) and scalar-inducedgravitational waves (that could reproduce the recent Pulsar Timing Arrayobservation, or predict signals in future detectors such as LISA or ET).Spectral signatures depend on whether the inflaton mass dimension at the poleis above or below 2. Values mildly below 2 allow a big power spectrumenhancement with a mild tuning. Finally, we discuss the possibility that akinetic pole can arise as anomalous dimension of the inflaton due to quantumeffects of Planckian particles that become light at some specific inflatonfield value.

Traversing a kinetic pole during inflation: primordial black holes and gravitational waves