Particle production from oscillating scalar field and consistency of Boltzmann equation

Boltzmann equation plays important roles in particle cosmology in studying the evolution of distribution functions (also called as occupation numbers) of various particles. For the case of the decay of a scalar condensation ϕ into a pair of scalar particles (called χ), we point out that the system may not be well described by the Boltzmann equation when the occupation number of χ becomes large even in the so-called narrow resonance regime. We study the particle production including the possible enhancement due to a large occupation number of the final state particle, known as the stimulated emission or the parametric resonance. Based on the quantum field theory (QFT), we derive a set of equations which directly govern the evolution of the distribution function of χ. Comparing the results of the QFT calculation and those from the Boltzmann equation, we find non-agreements in some cases. In particular, in the expanding Universe, the occupation number of χ based on the QFT may differ by many orders of magnitude from that from the Boltzmann equation. We also discuss a possible relation between the evolution equations based on the QFT and the Boltzmann equation.