CMB and random flights: temperature and polarization in position space

Journal Article · Sat Jun 01 04:00:00 EDT 2013 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2013/06/043· OSTI ID:22282778

Reimberg, Paulo H.F.

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.

• OSTI ID: 22282778
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 06 Vol. 2013; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
ANISOTROPY
ASTROPHYSICS
ASYMPTOTIC SOLUTIONS
BOLTZMANN EQUATION
COSMOLOGY
DENSITY
FLUCTUATIONS
H THEOREM
PHOTONS
POLARIZATION
PROBABILITY
RANDOMNESS
RELICT RADIATION
SPACE