Exponential Growth of Particle Number far from the Parametric Resonance Regime

Parametric resonance has received a considerable amount of interest as a good mathematical model to describe the initial stages of the reheating phase (matter creation) in inflationary cosmology. It is also known that exponential particle creation can occur in situations which do not fall in the parametric resonance regime characterized by oscillations of the inflaton field about its minimum. Here we present a new analytical approach to exponential particle production which can occur when the inflaton is far from the minimum of its potential. Crucial for this effect is a term in the equation of motion which acts like a negative mass square term, as occurs for tachyonic preheating and negative coupling particle production. Our techniques apply in models with a strong coupling between matter fields $\chi$ and the inflaton $\phi$, or in some models in which the inflaton has a large amplitude of oscillation. Note that our analysis yields results which are quite model dependent. Exponential growth occurs in a model with interaction Lagrangian $-g M_{pl}\phi\chi^2$. However, for the interaction Lagrangian $-g^2\phi^2\chi^2$, our formalism shows that in the large coupling limit there can only be exponential particle production when $\phi$ crosses 0.