A Smooth Landscape: Ending Saddle Point Inflation Requires Features to
  be Shallow
  We consider inflation driven near a saddle point in a higher dimensional
field space, which is the most likely type of slow roll inflation on the string
theoretical landscape; anthropic arguments need to be invoked in order to find
a sufficiently flat region. To give all inflatons large masses after inflation
and yield a small but positive cosmological constant, the trajectory in field
space needs to terminate in a hole on the inflationary plateau, introducing a
curved end-of-inflation hypersurface. We compute non-Gaussianities (bi- and
tri-spectrum) caused by this curved hyper-surface and find a negative,
potentially large, local non-linearity parameter. To be consistent with current
observational bounds, the hole needs to be shallow, i.e. considerably wider
than deep in natural units. To avoid singling out our vacuum as special (i.e.
more special than a positive cosmological constant entails), we deduce that all
features on field space should be similarly shallow, severely limiting the type
of landscapes one may use for inflationary model building.
  We justify the use of a truncated Fourier series with random coefficients,
which are suppressed the higher the frequency, to model such a smooth landscape
by a random potential, as is often done in the literature without a good a
priory reason.
