  We study the prospects of detection at terrestrial and space interferometers,
as well as at pulsar timing array experiments, of a stochastic gravitational
wave background which can be produced in models of axion inflation. This
potential signal, and the development of these experiments, open a new window
on inflation on scales much smaller than those currently probed with Cosmic
Microwave Background and Large Scale Structure measurements. The sourced signal
generated in axion inflation is an ideal candidate for such searches, since it
naturally grows at small scales, and it has specific properties (chirality and
non-gaussianity) that can distinguish it from an astrophysical background. We
study under which conditions such a signal can be produced at an observable
level, without the simultaneous overproduction of scalar perturbations in
excess of what is allowed by the primordial black hole limits. We also explore
the possibility that scalar perturbations generated in a modified version of
this model may provide a distribution of primordial black holes compatible with
the current bounds, that can act as a seeds of the present black holes in the
universe.
