Far-from-equilibrium kinetic dynamics of λ?4 theory in an expanding universe

We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar field particles with quartic (tree level) self-interactions (lambda phi 4) in Friedmann-Lemaitre-Robertson-Walker spacetime. Using a new covariant generating function for the moments of the Boltzmann distribution function, we analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator. We show how the covariant generating function can be also used to find the exact equations for the moments in the full nonlinear regime. Different than the case of a ultrarelativistic gas of hard spheres (where the total cross section is constant), for lambda phi 4 the fact that the cross section decreases with energy implies that moments of arbitrarily high order directly couple to low order moments. Numerical solutions for the scalar field case are presented and compared to those found for a gas of hard spheres.

Automated summary

We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar field particles with quartic self-interactions (lambda phi 4) in Friedmann-Lemaitre-Robertson-Walker spacetime. We analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator using a new covariant generating function. Our results show that the cross section of lambda phi 4 decreases with energy, leading to direct coupling between moments of different orders. Numerical solutions for the scalar field case are provided and compared to those of a gas of hard spheres.