  After cosmic inflation and before the transition to radiation domination, the
cosmic energy density may have been dominated during an extended period by an
oscillating massive scalar condensate. We show that during this period,
sub-Hubble scale perturbations are subject to a metric preheating instability
in the narrow resonance regime. We analyze in detail both, quadratic and
quartic potentials. The instability leads to the growth of density
perturbations which in many cases become non-linear already before the
beginning of a radiation dominated Universe. This is particularly the case when
requiring a phenomenologically preferred low reheat temperature. These early
structures may lead to the emission of gravitational waves and the production
of primordial black holes. Furthermore, it is not clear if they could modify
the prediction of linear curvature perturbations on very large scales.
