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Westudythebehaviourofisocurvatureperturbationsinnon-linearsigmamodels whichnaturally emerge in supergravity and string inflationary scenarios. We focus onthe case of negatively curved field manifolds which can potentially lead to ageometrical destabilisation of isocurvature modes. We find however that heavyfields are stable when their effective mass is computed on the attractorbackground solution. On the other hand, we show that ultra-light fields canpotentially suffer from a geometrical instability when the backgroundtrajectory is a geodesic in field space. In this case a full understanding ofthe system is likely to require the use of non-perturbative methods.

A geometrical instability for ultra-light fields during inflation?