Global in time stability of equilibrium for general relativistic Boltzmann equation in the massless Robertson-Walker spacetime

The general relativistic Boltzmann equation is a fundamental physical model in astrophysics, for example in systems of galaxies, in supernova explosions, as a model of the early universe, and additionally as a model for hot gasses and plasmas.  The general relativistic Boltzmann equation with the Robertson-Walker metric in the massless case admits a family of non-stationary Equilibria of the form $J((t^q)^2 p) = \exp(-(t^q)^2 |p|)$.  The Robertson-Walker metric, or Friedmann–Lemaître–Robertson–Walker metric, is a widely used model describing a homogeneous isotropic and expanding universe.  In this work, for $0< q < 1$, we prove the global-in-time existence and uniqueness of suitably small perturbations of these Equilibria.  For $0< q < 1/3$ we prove that the perturbation has the superpolynomial large time-decay rate of $\exp(-t^{1-3q})$, and for $1/3< q < 1$ the perturbation has a slower time-decay rate of $t^{-3q}$.

This is a joint work with Martin Taylor and Renato Velozo Ruiz (both of Imperial College in London).

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