Relativistic Gas In De Sitter Spacetime

Relativistic gas is an old topic, it is used in plasma physics,astrophysics and cosmology.After the model of Marle for the collision operator of the Boltzmann equation was built, more and more papers were published by scientists. The relativistic Boltzmann equation was discussed,First, the Boltzmann equation was built in the condition of relativistic, then we study the relativistic gas of the Boltzmann equation in de Sitter spacetime.It is use the Chapman-Enskog method that the nonequilibrium count as the Maxwell-J¨uttner distribution function and the deviation of the Maxwell-J¨uttner distribution function. we can get the particle four-?ow,the energy-momentum tensor,particle number density and energy per particle.Then we get the coe?cients of thermal conductivity and viscosities.The reason for our special attention to de Sitter spacetime stems from the fact that de Sitter spacetime is the unique maximally symmetric curved spacetime. It enjoys the same degree of symmetry as Minkowski spacetime(ten Killing vectors).Besides, the current observations, together with the theory of in?ation, suggest that our universe may have approached de Sitter geometries in the far past and may approach de Sitter geometries in the far future.We study the relativistic gas in de Sitter spacetime by using the model of Marle. We ?nd that the momentum balance equation is a?ected by the gravitational ?eld, and in the non-relativistic regime it reduces to the usual expression of Newton’s second law. We note that the coe?cients of thermal conductivity and viscosities depend on the gravitational ?eld, and they increase as the gravitational becomes stronger. We also show that, apart from the temperature gradient, the Fourier’s law has two relativistic terms, one dues to the inertia of the energy, while the other is related to the cosmical constant.