Abstract
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.
Highlights
Observations indicate that a substantial part of the energy budget of the Universe is made up of dark matter
While isotropy and homogeneity constrain the cosmological background dynamics to be of perfect fluid type [3], gravitational collapse is caused by fluctuations which are expected to generate nonvanishing shear stress at smaller scales and require a nonideal fluid description
Starting from a general relativistic kinetic theory approach for a system of collisionless classical point particles we presented the method of moments and cumulants of the one-particle phase-space distribution function
Summary
Observations indicate that a substantial part of the energy budget of the Universe is made up of dark matter. At a given finite order, this leads to additional constraint equations that related the components of the conserved currents to the hydrodynamic fields Such a gradient expansion is well motivated in the vicinity of thermal equilibrium or when interaction effects are so strong that they quickly drive the system back towards local equilibrium when the latter is violated as a consequence of fluid motion. This leads to a formalism with more dynamical variables or fluid fields, for example shear stress, bulk viscous pressure, heat current or particle diffusion current Such additional evolution equations have been first obtained from a kinetic theory approach where the system is characterized by a phase-space distribution function which obeys the relativistic Boltzmann equation.
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