从Vlasov-Einstein方程导出暗物质相空间密度和Jeans尺度的演化
Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation
摘要：
在平坦的Friedmann宇宙中讨论了无碰撞暗物质粒子的Vlasov-Einstein方程解。我们表明，从原始等离子体去耦后，暗物质相空间密度指标Q保持恒定的宇宙膨胀过程中，结构形成之前。这个众所周知的结果对非相对论性粒子是有效的，并且不像从弗拉索夫-泊松系统导出的解那样是“依赖于观察者”的。在线性区域中，考虑速度色散效应，可以定义无碰撞物质的物理金斯长度为原始相空间密度指示器的函数：λ_J =（5π/G）^（1/2）Q^（-1/3）ρ_dm^（-1/6）。在物质辐射相等时的同向Jeans波数比自由流的同向波数小2-3倍，有助于在最低尺度处截断密度波动功率谱。我们讨论这两种尺度之间的物理差异。对于质量等于200 GeV的暗物质粒子，导出的金斯质量是4.3 x 10^（-6）太阳质量。
英文摘要：
We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not "observer dependent" as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: λ_J = (5π/G)^(1/2)Q^(-1/3)ρ_dm^(-1/6). The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 x 10^(-6) solar masses.
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