  Particle production and its effects on the inflaton field are investigated
during the preheating phase of chaotic inflation using a model consisting of a
massive scalar inflaton field coupled to N massless quantum scalar fields. The
effects of spacetime curvature and interactions between the quantum fields are
ignored. A large N expansion is used to obtain a coupled set of equations
including a backreaction equation for the classical inflaton field. Previous
studies of preheating using these equations have been done. Here the first
numerical solutions to the full set of equations are obtained for various
values of the coupling constant and the initial amplitude of the inflaton
field. States are chosen so that initially the backreaction effects on the
inflaton field are small and the mode equations for the quantum fields take the
form of Mathieu equations. Potential problems relating to the parametric
amplification of certain modes of the quantum fields are identified and
resolved. A detailed study of the damping of the inflaton field is undertaken.
Some predictions of previous studies are verified and some new results are
obtained.
