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.
Cite
@article{arxiv.1303.7258,
title = {CMB and Random Flights: temperature and polarization in position space},
author = {Paulo H. F. Reimberg and L. Raul Abramo},
journal= {arXiv preprint arXiv:1303.7258},
year = {2013}
}
Comments
Minor revisions; matches version published in JCAP06(2013)043