  Inflation ends with the formation of a Bose condensate of inflatons. We show
that in hybrid inflation models this condensate is typically unstable with
respect to spatial perturbations and can fragment to condensate lumps. The case
of D-term inflation is considered as an example and it is shown that
fragmentation occurs if \lambda > 0.2g, where \lambda is the superpotential
coupling and g is the U(1)_{FI} gauge coupling. Condensate fragmentation can
result in an effective enhancement of inflaton annihilations over decays as the
main mode of reheating. In the case of D-term inflation models in which the
Standard Model fields carry U(1)_{FI} charges, if condensate fragmentation
occurs then reheating is dominated by inflaton annihilations, typically
resulting in the overproduction of thermal gravitinos. Fragmentation may also
have important consequences for SUSY flat direction dynamics and for
preheating.
