  The Standard Model Higgs potential may become unbounded from below at large
field values, with important cosmological implications. For a potential of this
form, the commonly assumed scenario of a nucleated thin-wall bubble driving the
transition from the electroweak vacuum to the unstable region does not apply.
We present exact analytical solutions for potentials that have the same
qualitative form as the Higgs potential. They show that the transition is
driven by a thick-wall spherical bubble of true vacuum, with a surface that
expands at asymptotically the speed of light. A `crunch' singularity appears in
the quasi-AdS interior, with the collapsed region also expanding at
asymptotically the speed of light. The singularity is surrounded by a region of
trapped surfaces whose boundary forms an apparent horizon. An event horizon
separates the singularity from the bubble exterior, so that the expansion of
the bubble surface is not affected by the collapse of the interior. The
solutions provide exact descriptions of the geometry for thick-wall bubbles and
are consistent with the analysis of [1,2] for the Higgs potential.
