CMB and Random Flights: temperature and polarization in position space

Abstract : 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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Paulo H. F. Reimberg, L. Raul Abramo. CMB and Random Flights: temperature and polarization in position space. Journal of Cosmology and Astroparticle Physics, Institute of Physics (IOP), 2013, 06, pp.043. ⟨10.1088/1475-7516/2013/06/043⟩. ⟨cea-01333494⟩

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