Primordial Black Holes (PBH) from peaks in the curvature power spectrum could constitute today an important fraction of the Dark Matter in the Universe. At horizon reentry, during the radiation era, order one fluctuations collapse gravitationally to
form black holes and, at the same time, generate a stochastic background of gravitational waves coming from second order anisotropic stresses in matter. We study the amplitude and shape of this background for several phenomenological models of the curvature power spectrum that can be embedded in waterfall hybrid inflation, axion, domain wall, and boosts of PBH formation at the QCD transition. For a broad peak or a nearly scale invariant spectrum, this stochastic background is generically enhanced by about one order of magnitude, compared to a sharp feature. As a result, stellar-mass PBH from Gaussian fluctuations with a wide mass distribution are already in strong tension with the limits from Pulsar Timing Arrays, if they constitute a non negligible fraction of the Dark Matter. But this result is mitigated by the uncertainties on the curvature threshold leading to PBH formation. LISA will have the sensitivity to detect or rule out light PBH down to $10^{-14} M_{odot}$. Upcoming runs of LIGO/Virgo and future interferometers such as the Einstein Telescope will increase the frequency lever arm to constrain PBH from the QCD transition. Ultimately, the future SKA Pulsar Timing Arrays could probe the existence of even a single stellar-mass PBH in our Observable Universe.
The observational signatures of multi-field inflation will generally evolve as the Universe reheats. We introduce a general analytic formalism for tracking this evolution through perturbative reheating, applicable to two field models with arbitrary s
eparable potentials. The various transitions, including the onset of scalar field oscillations and the reheating of each field, can happen in different orders and on arbitrary hypersurfaces. The effective equations of state of the oscillating fields are also arbitrary. Nevertheless, our results are surprisingly simple. Our formalism encapsulates and generalises a huge range of previous calculations including two-field inflation, spectator models, the inhomogeneous end of inflation scenario and numerous generalised curvaton scenarios.
