Anisotropies in the cosmic microwave background: an analytic approach

Abstract

We i n troduce a simple yet powerful analytic method which obtains the structure of cosmic microwave background anisotropies to better than 5-10% in temperature uctuations on all scales. It is applicable to any model in which the potential uctuations at recombination are both linear and known. Moreover, it recovers and explains the presence of the \Doppler peaks" at degree scales as driven acoustic oscillations of the photon-baryon uid. 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 i n to the anisotropies, including the dependence of the peak locations and heights on cosmological parameters such a s b and h, a s w ell as model parameters such as the ionization history. Damping due to the nite thickness of the last scattering surface and photon diusion are further more shown to be identical. 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 uctuations is satisfactory and/or speed is essential. Equally importantly, it can be used as a portable standard by which n umerical codes can be tested and compared.

Cosmic microwave background anisotropy with cosine-type quintessence

“…If q is non-vanishing, the energy density of the quintessence field fluctuates. The energy density, pressure, and momentum perturbations of the quintessence are given by 20) respectively. These perturbations will affect the density perturbation of the universe and may change the behavior of the CMB anisotropy, as will be discussed in the following section.…”

“…The locations of the peaks depend on two quantities, the sound horizon at last scattering and the angular diameter distance to the last scattering surface. Approximately, the l-th multipole picks up scales around l ∼ kr θ (τ * ) where r θ (τ * ) is the angular diameter distance to the last scattering surface [20]. The n-th peak in the temperature power spectrum is located at the scale k n which satisfies k n r s (τ * ) = nπ, where r s (τ * ) is the sound horizon at last scattering.…”

Interacting photon–baryon fluid, warm dark matter, and the first acoustic peak

“…As a result one obtains an equation for the density contrast with the help of which it is possible to derive an expression for the position of the first acoustic peak. In the standard model this position is well determined by the fit given by Hu and Sugiyama [21]. Although it is strictly valid only for the CDM model, we can use this fit her as well because values ξ < 10 −3 are suggested from observational constraints on the sound horizon r s .…”

“…Originally this approximation was implemented by Peebles and Yu [20] (see also Hu and Sugiyama [21]). Following Ref.…”

VSL theories and the Doppler peak

“…The precise form of the Doppler peak depends on the nature of the dark matter and the values of Ω 0 , Ω b and H 0 . The scale l p of the main peak reflects the size of the horizon at last scattering of the CMB photons and thus depends almost entirely [28,31] on the total density of the universe according to…”