  We present fully non-linear simulations of a self-interacting scalar field in
the early universe undergoing tachyonic preheating. We find that density
perturbations on sub-horizon scales which are amplified by tachyonic
instability maintain long range correlations even during the succeeding
parametric resonance, in contrast to the standard models of preheating
dominated by parametric resonance. As a result the final spectrum exhibits
memory and is not universal in shape. We find that throughout the subsequent
era of parametric resonance the equation of state of the universe is almost
dust-like, hence the Jeans wavelength is much smaller than the horizon scale.
If our 2D simulations are accurate reflections of the situation in 3D, then
there are wide regions of parameter space ruled out by over-production of black
holes. It is likely however that realistic parameter values, consistent with
COBE/WMAP normalisation, are safetly outside this black hole over-production
region.
