Particle Production from Oscillating Scalar Field and Consistency of Boltzmann Equation

Abstract: 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 $\phi$ into a pair of scalar particles (called $\chi$), we point out that the system may not be well described by the Boltzmann equation when the occupation number of $\chi$ 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 $\chi$. 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 $\chi$ 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.