Fatal youth of the Universe: black hole threat for the electroweak vacuum during preheating
Small evaporating black holes were proposed to be dangerous inducing fast decay of the electroweak false vacuum. We observe that the flat-spectrum matter perturbations growing at the post-inflationary matter dominated stage can produce such black holes in a tiny amount which may nevertheless be sufficient to destroy the vacuum in the visible part of the Universe via the induced process. If the decay probability in the vicinity of Planck-mass black holes was of order one as suggested in literature, the absence of such objects in the early Universe would put severe constraints on inflation and subsequent stages thus excluding many well-motivated models (e.g. the R^2-inflation) and supporting the need of new physics in the Higgs sector. We give a qualitative argument, however, that exponential suppression of the probability should persist in the limit of small black hole masses. This suppression relaxes our cosmological constraints, and, if sufficiently strong, may cancel them.