  A new truncation scheme based on the cumulant expansion of the one-particle
phase-space distribution function for dark matter particles is developed.
Extending the method of moments in relativistic kinetic theory, we derive
evolution equations which supplement the covariant conservation of the
energy-momentum tensor and particle number current. Truncating the cumulant
expansion we obtain a closed, covariant and hyperbolic system of equations
which can be used to model the evolution of a general relativistic non-ideal
fluid. As a working example we consider a Friedmann-Lema\^itre-Robertson-Walker
cosmology with dynamic pressure and solve for the time evolution of the
effective equation of state parameter.
