Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$

Details Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$ Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$

2001-03-19

arxiv.org/abs/astro-ph/0103281v2

Phys.Rev. D64 (2001) 123512

Astronomy and Astrophysics

Astrophysics

16 pages, one inessential figure. Improved treatment of damping in companion paper used here in calculations, reference added,

Scientific paper

10.1103/PhysRevD.64.123512

General asymptotic formulas are given for the coefficient $C_\ell$ of the term of multipole number $\ell$ in the temperature correlation function of the cosmic microwave background, in terms of scalar and dipole form factors introduced in a companion paper. The formulas apply in two overlapping limits: for $\ell\gg 1$ and for $\ell d/d_A\ll 1$ (where $d_A$ is the angular diameter distance of the surface of last scattering, and $d$ is a length, of the order of the acoustic horizon at the time of last scattering, that characterizes acoustic oscillations before this time.) The frequently used approximation that $C_\ell$ receives its main contribution from wave numbers of order $\ell/d_A$ is found to be less accurate for the contribution of the Doppler effect than for the Sachs--Wolfe effect and intrinsic temperature fluctuations. For $\ell d/d_A\ll 1$ and $\ell\geq 2$, the growth of $C_\ell$ with $\ell$ is shown to be affected by acoustic oscillation wave numbers of all scales. The asymptotic formulas are applied to a model of acoustic oscillations before the time of last scattering, with results in reasonable agreement with more elaborate computer calculations.

Affiliated with

Also associated with

No associations

Rating

Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-2108