  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.
