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Anisotropies in the cosmic microwave background: an analytic approach
Hu, Wayne; Sugiyama, Naoshi
AA(University of California, Berkeley, California, US), AB(University of California, Berkeley, California, US)
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 444, no. 2, p. 489-506 (ApJ Homepage)
Publication Date:
NASA/STI Keywords:
Anisotropy, Astronomical Models, Background Radiation, Cosmic Rays, Cosmology, Microwaves, Temperature Gradients, Baryons, Boltzmann Distribution, Dark Matter, Doppler Effect, Gravitational Effects, Photons
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We introduce a conceptually simple yet powerful analytic method which traces the structure of cosmic microwave background anisotropies to better than 5%-10% in temperature fluctuations on all scales. It is applicable to any model in which the gravitational potential is known and last scattering is sufficiently early. Moreover, it recovers and explains the presence of the 'Doppler peaks' at degree scales as driven acoustic oscillations of the photon-baryon fluid. We treat in detail such subtleties as the time dependence of the gravitational driving force, anisotropic stress from the neutrino quadrupole, and damping during the recombination process, again all from an analytic standpoint. We apply this formalism to the standard cold dark matter model to gain physical insight into the anisotropies, including the dependence of the peak locations and heights on cosmological parameters such as Omegab and h. Furthermore, the ionization history controls damping due to the finite thickness of the last scattering surface, which is in fact mianly caused by photon diffusion. In addition to being a powerful probe into the nature of anisotropies, this treatment can be used in place of the standard Boltzmann code where 5%-10% accuracy in temperature fluctuations is satisfactory and/or speed is essential. Equally importantly, it can be used as a portable standard by which numerical codes can be tested and compared.

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