Lukewarm inflation, primordial black holes and gravitational waves

We show that a secondary period of warm inflation, at temperatures parametrically below the GUT scale, may not only dilute any unwanted thermal relics formed after reheating but also significantly enhance the power spectrum of primordial curvature perturbations on small scales. The latter is nearly scale-invariant over an exponentially large range of comoving scales, resulting in a stochastic gravitational wave background with a nearly constant energy density over a broad range of frequencies and an associated population of sub-solar mass primordial black holes (PBHs). This scenario could, in particular, explain the NANOGrav signal if it persists at much higher frequencies with a comparable magnitude, up to a sharp cut-off, f max. The associated PBH mass distribution may exhibit either a peak at a mass M* proportional to f max-2 or a broad plateaux above this mass threshold, depending on the spectral tilt. Moreover, in this scenario the NANOGrav signal is compatible with a significant fraction of dark matter in PBHs in the asteroid- and planetary-mass ranges.