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

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