  If the universe is trapped and cooled in a metastable false vacuum state,
that state will eventually decay by bubble nucleation and expansion. For
example, many extensions of the standard model incorporate new scalar fields
whose potential has a local minimum at the origin but a global minimum
elsewhere, to which the vacuum will eventually tunnel. I calculate the lifetime
of the false vacuum, and the field profile of the bubble after tunneling, for
any potential that is approximately a polynomial of degree <= 4 near the false
vacuum. Essentially exact results are given for a single field; for multiple
fields the given action is a strict upper bound.
