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The Lyth Bound and the End of Inflation
We derive an extended version of the well-known Lyth Bound on the total
variation of the inflaton field, incorporating higher order corrections in slow
roll. We connect the field variation to both the spectral index of
scalar perturbations and the amplitude of tensor modes. We then investigate the
implications of this bound for ``small field'' potentials, where the field
rolls off a local maximum of the potential. The total field variation during
inflation is {\em generically} of order , even for potentials with
a suppressed tensor/scalar ratio. Much of the total field excursion arises in
the last e-fold of inflation and in single field models this problem can only
be avoided via fine-tuning or the imposition of a symmetry. Finally, we discuss
the implications of this result for inflationary model building in string
theory and supergravity.Comment: 10 pages, RevTeX, 2 figures (V3: version accepted for publication by
JCAP