The cosmic microwave background radiation (CMBR) fractional temperature
perturbation, , is expressed as a function of angular position,
, on the sky via the spherical harmonic decomposition,
Given a gaussian model , the predicted root mean square (rms)
temperature that would be measured by an experiment,
is defined by
It has become conventional to summarize zero-lag window functions in terms
of a few parameters (e.g., Bond; Ratra et al.). These are the value of
where is greatest, , the two values of ,
It is of interest to use anisotropy observations to measure the power
spectrum over the entire range of to which an experiment is
sensitive. However, the broad width of the window functions of
current experiments prevents determination of each individual
. To analyze experimental data it is therefore necessary to
assume a functional form for the 's over the range of the
experiment is sensitive to, with the overall normalization allowed to
be a free parameter and with the shape of the allowed to depend
on a small number of other parameters. Comparing these 's to the
data then allows for a determination of the normalization and of the shape
parameters which best agree with the data.
Most analyses of data make use of the flat angular power spectrum,
J.R. Bond, ``Theory and Observations of the Cosmic Background Radiation", in
Cosmology and Large Scale Structure, ed. R. Schaeffer, J. Silk, M. Spiro,
and J. Zinn-Justin (Amsterdam: Elsevier Science), 469 (1996).
P.J.E. Peebles, ``Large-Scale Background Temperature and Mass Fluctuations due to Scale-Invariant Primeval Perturbations", Astrophys. J. Lett. 263, L1 (1982).
B. Ratra, N. Sugiyama, A.J. Banday, and K.M. Górski, ``Cosmic Microwave Background Anisotropy in DMR-Normalized Open and Flat- Cold Dark Matter Cosmogonies", Astrophys. J. 481, 22 (1997).