= Waterfall instability in F-term hybrid inflation
{title2=$m_\pm^2\simeq|g|^2(|S|^2\pm|\zeta|)$}
In the small-field global approximation, the waterfall fluctuations on $u=v=0$ have the displayed masses. One becomes negative when $|S|^2<|\zeta|$, driving the fields towards the <supersymmetric vacuum> branch. In the canonical supergravity model, the exact masses follow from expanding the exponential and Kähler-covariant derivatives; their Planck-suppressed corrections should not be discarded unless the corresponding field and symmetry-breaking scales are small.
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