Far-from-equilibrium kinetic dynamics of $\lambda {\varphi }^4$ theory in an expanding universe

Abstract

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 ($\lambda {\varphi }^4$) 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 $\lambda {\varphi }^4$ 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.

19 pages, 5 figures

References in corpus (13)

• Quasi-Particle Theory of Shear and Bulk Viscosities of Hadronic Matter
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Bulk viscosity in quasi particle models
• Universality far from equilibrium: From superfluid Bose gases to heavy-ion collisions
• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation
• Non-equilibrium attractor in high-temperature QCD plasmas
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
• Perturbative approaches in relativistic kinetic theory and the emergence of first-order hydrodynamics
• Exponential Approach to the Hydrodynamic Attractor in Yang-Mills Kinetic Theory
• Transport coefficients of quasi-particle models within a new relaxation time approximation of the Boltzmann equation
• Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow

Cited by in corpus (6)

• The Present and Future of QCD
• Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: microscopic derivations and attractors
• Analytical structure of the binary collision integral and the ultrarelativistic limit of transport coefficients of an ideal gas
• Modelling stochastic fluctuations in relativistic kinetic theory
• Infinite Order Hydrodynamics: An Analytical Example
• Field Theory Approaches to Relativistic Hydrodynamics