We analyze primordial non-gaussianities in presence of an ultra-slow phase during the inflationary dynamics, focusing on scenarios relevant for the production of primordial black holes. We compute the three-point correlation function of comoving curvature perturbations finding that non-gaussianities are sizable, and predominantly local. In the context of threshold statistics, we analyze their impact for the abundance of primordial black holes, and their interplay with the non-gaussianities arising from the non-linear relation between density and curvature perturbations. We find that non-gaussianities significantly modify the estimate of the primordial black holes abundance obtained with the gaussian approximation. However, we show that this effect can be compensated by a small change, of a factor 2÷3 at most, of the amplitude of the primordial power spectrum of curvature perturbations. This is obtained with a small tuning of the parameters of the inflationary model.

We discuss a class of Dark Matter (DM) models that, although inherently strongly coupled, appear weakly coupled at small-energy and fulfill the WIMP miracle, generating a sizable relic abundance through the standard freeze-out mechanism. Such models are based on approximate global symmetries that forbid relevant interactions; fundamental principles, like unitarity, restrict these symmetries to a small class, in such a way that the leading interactions between DM and the Standard Model are captured by effective operators up to dimension-8. The underlying strong coupling implies that these interactions become much larger at high-energy and represent an interesting novel target for LHC missing-energy searches.

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