Eternal Hilltop Inflation
  We consider eternal inflation in hilltop-type inflation models, favored by
current data, in which the scalar field in inflation rolls off of a local
maximum of the potential. Unlike chaotic or plateau-type inflation models, in
hilltop inflation the region of field space which supports eternal inflation is
finite, and the expansion rate $H_{EI}$ during eternal inflation is almost
exactly the same as the expansion rate $H_*$ during slow roll inflation.
Therefore, in any given Hubble volume, there is a finite and calculable
expectation value for the lifetime of the "eternal" inflation phase, during
which quantum flucutations dominate over classical field evolution. We show
that despite this, inflation in hilltop models is nonetheless eternal in the
sense that the volume of the spacetime at any finite time is exponentially
dominated by regions which continue to inflate. This is true regardless of the
energy scale of inflation, and eternal inflation is supported for inflation at
arbitrarily low energy scale.
