  We show the existence of a general mechanism by which heavy scalar fields can
be destabilized during inflation, relying on the fact that the curvature of the
field space manifold can dominate the stabilizing force from the potential and
destabilize inflationary trajectories. We describe a simple and rather
universal setup in which higher-order operators suppressed by a large energy
scale trigger this instability. This phenomenon can prematurely end inflation,
thereby leading to important observational consequences and sometimes excluding
models that would otherwise perfectly fit the data. More generally, it modifies
the interpretation of cosmological constraints in terms of fundamental physics.
We also explain how the geometrical destabilization can lead to powerful
selection criteria on the field space curvature of inflationary models.
