We consider the possibility that the majority of dark matter in our Universe consists of black holes of primordial origin. We determine the conditions under which such black holes may have originated from a single-field model of inflation characterized by a quartic polynomial potential. We also explore the effect of higher-dimensional operators. The large power spectrum of curvature perturbations that is needed for a large black hole abundance sources sizable second order tensor perturbations. The resulting stochastic background of primordial gravitational waves could be detected by the future space-based observatories LISA and DECIGO or—as long as we give up on the dark matter connection—by the ground-based Advanced LIGO-Virgo detector network.

We consider the impact of quantum diffusion on inflationary dynamics during an ultra-slow-roll phase, which can be of particular significance for the formation of primordial black holes. We show, by means of a fully analytical approach, that the power spectrum of comoving curvature perturbations computed in stochastic inflation matches precisely, at the linear level, the result obtained by solving the Mukhanov-Sasaki equation, even in the presence of an ultra-slow-roll phase. We confirm this result numerically in a model in which the inflaton has a polynomial potential and is coupled quadratically to the Ricci scalar. En route, we assess the role that quantum noise plays in the presence of an ultra-slow-roll phase, and clarify the issue of the quantum-to-classical transition in this scenario.

We present a scenario that ameliorates the tuning problems present in models of primordial black hole (PBH) dark matter from inflation. Our setup employs the advantages of gravitational collapse in a long epoch of early matter domination with reheating temperature ≲ 106 GeV. Furthermore, we make use of a string-inspired class of models where the inflaton is identified with a non-compact axion field. In this framework, the presence of multiple local minima in the inflaton potential can be traced back to an approximate discrete shift symmetry. This scenario allows the formation of PBHs in the observationally viable range of masses (MPBH∼ 10−16M⊙–10−13M⊙) accounting for all dark matter, and in excellent agreement with the CMB . We find a significant reduction in the required tuning of the parameters of the inflationary potential, in contrast to the standard case of PBH formation during radiation domination. However, abundant formation of light PBHs during an early phase of matter domination can be more easily in conflict with evaporation bounds. We discuss how these can be avoided under mild assumptions on the collapsing energy density fraction.