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.
