  We propose a new class of inflationary solutions to the standard cosmological
problems (horizon, flatness, monopole,...), based on a modification of old
inflation. These models do not require a potential which satisfies the normal
inflationary slow-roll conditions. Our universe arises from a single tunneling
event as the inflaton leaves the false vacuum. Subsequent dynamics (arising
from either the oscillations of the inflaton field or thermal effects) keep a
second field trapped in a false minimum, resulting in an evanescent period of
inflation (with roughly 50 e-foldings) inside the bubble. This easily allows
the bubble to grow sufficiently large to contain our present horizon volume.
Reheating is accomplished when the inflaton driving the last stage of inflation
rolls down to the true vacuum, and adiabatic density perturbations arise from
moduli-dependent Yukawa couplings of the inflaton to matter fields. Our
scenario has several robust predictions, including virtual absence of gravity
waves, a possible absence of tilt in scalar perturbations, and a higher degree
of non-Gaussianity than other models. It also naturally incorporates a solution
to the cosmological moduli problem.
