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arXiv 1303.7258astro-ph.COcond-mat.stat-mechmath-phmath.MP
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CMB和随机飞行:位置空间中的温度和偏振

CMB and Random Flights: temperature and polarization in position space

Paulo H. F. Reimberg, L. Raul Abramo

摘要:

宇宙微波背景的温度和偏振的涨落由玻尔兹曼方程描述。在积分形式中,玻尔兹曼层次可以从通常的傅立叶空间基转换为位置空间和因果描述。我们表明,随机航班的概率密度在这种描述中发挥了关键作用。积分系统可以被视为随机飞行步数的摄动级数,随机飞行概率的性质对依赖域施加了约束。我们表明,由于这些领域,傅立叶-贝塞尔分解可以用来计算随机飞行概率密度。我们还说明了如何H定理适用于宇宙微波背景:通过使用这些概率密度的渐近极限的解析公式,我们表明,作为光子分布接近平衡状态,温度各向异性和净偏振必须消失。

英文摘要:

The fluctuations in the temperature and polarization of the cosmic microwave background are described by a hierarchy of Boltzmann equations. In its integral form, this Boltzmann hierarchy can be converted from the usual Fourier-space base into a position-space and causal description. We show that probability densities for random flights play a key role in this description. The integral system can be treated as a perturbative series in the number of steps of the random flights, and the properties of random flight probabilities impose constraints on the domains of dependence. We show that, as a result of these domains, a Fourier-Bessel decomposition can be employed in order to calculate the random flight probability densities. We also illustrate how the H-theorem applies to the cosmic microwave background: by using analytical formulae for the asymptotic limits of these probability densities, we show that, as the photon distribution approaches a state of equilibrium, both the temperature anisotropies and the net polarization must vanish.

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