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 nonideal fluid. As a working example we consider a Friedmann-Lemaître-Robertson-Walker cosmology with dynamic pressure and solve for the time evolution of the effective equation of state parameter.
A. Erschfeld, S. Floerchinger, and M. Rupprecht, “General relativistic nonideal fluid equations for dark matter from a truncated cumulant expansion”, Phys. Rev. D 102, 063520 (2020).
Related to Project: C06