The figure on the left shows first results for the
evolution of the matter field fluctuations and the metric
perturbations, for the simple case of a massive inflaton
with quadratic coupling to another scalar field. From
these calculations, presented in detail in
we conclude that, contrary to some other claims in the literature, metric
perturbations at least on scales relevant for structure
formation, are not strongly modified during preheating
and certainly do not grow non-linear.
We began to investigate preheating in the context of more general inflaton and matter field potentials. To this end a numerical code should be developed which takes into account as many nonlinear effects during preheating and reheating as possible. Preliminary results seem to indicate that significant increase of large scale metric fluctuations is possible in certain cases but typically requires considerable fine tuning of parameters. In the farther future this numerical tool should probably also be extended to fermions, gauge bosons, gravitinos etc.
Processes during reheating after inflation may also be important for the creation of superheavy particles and/or topological defects at the end of inflation which today may constitute non-thermal dark matter and whose decay may contribute to the ultrahigh energy cosmic ray flux.
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