Connecting the Higgs Potential and Primordial Black Holes
  It was recently demonstrated that small small black holes can act as seeds
for nucleating decay of the metastable Higgs vacuum, dramatically increasing
the tunneling probability. Any primordial black hole lighter than $4.5 \times
10^{14}$g at formation would have evaporated by now, and in the absence of new
physics beyond the standard model, would therefore have entered the mass range
in which seeded decay occurs, however, such true vacuum bubbles must percolate
in order to completely destroy the false vacuum; this depends on the bubble
number density and the rate of expansion of the universe. Here, we compute the
fraction of the universe that has decayed to the true vacuum as a function of
the formation temperature (or equivalently, mass) of the primordial black
holes, and the spectral index of the fluctuations responsible for their
formation. This allows us to constrain the mass spectrum of primordial black
holes given a particular Higgs potential and conversely, should we discover
primordial black holes of definite mass, we can constrain the Higgs potential
parameters.
