Non-Gaussianity in Two-Field Inflation
  We derive semi-analytic formulae for the local bispectrum and trispectrum in
general two-field inflation and provide a simple geometric recipe for building
observationally allowed models with observable non-Gaussianity. We use the
\delta N formalism and the transfer function formalism to express the
bispectrum almost entirely in terms of model-independent physical quantities.
Similarly, we calculate the trispectrum and show that the trispectrum parameter
\tau NL can be expressed entirely in terms of spectral observables, which
provides a new consistency relation unique to two-field inflation. We show that
in order to generate observably large non-Gaussianity during inflation, the
sourcing of curvature modes by isocurvature modes must be extremely sensitive
to the initial conditions, and that the amount of sourcing must be moderate in
order to avoid excessive fine-tuning. Under some minimal assumptions, we argue
that the first condition is satisfied only when neighboring trajectories
through the two-dimensional field space diverge during inflation.
Geometrically, this means that the inflaton must roll along a ridge in the
potential V for some time during inflation and that its trajectory must turn
slightly (but not too sharply) in field space. Therefore, it follows that
two-field scenarios with attractor solutions necessarily produce small
non-Gaussianity. This explains why it has been so difficult to achieve large
non-Gaussianity in two-field inflation, and why it has only been achieved in a
narrow class of models like hybrid inflation and certain product potentials
where the potential and/or the initial conditions are fine-tuned. Some of our
conclusions generalize qualitatively to general multi-field inflation.
