### angular power spectrum

(method of characterizing the CMB)

An **angular power spectrum** is a characterization of
a function on the surface of a sphere, or analogously,
all directions in space from a point. It captures variance
as a function of scale. An **angular two-point correlation**
does this, showing a correlation for each possible angle,
but the spectrum more often termed the *angular power spectrum*
is the correlation over each **multipole moment**
(i.e., **spherical harmonic order**), *l*
of a multipole expansion (analogous to a **Fourier series expansion**,
but for functions over the surface of a sphere).

The cosmic microwave background is often characterized by such an
*angular power spectrum* of its anisotropy,
showing the temperature variation for coefficients
of a multipole expansion of the temperature over the celestial sphere.
The temperature is calculated (in principle)
by Wien's displacement law from the received EMR
(in practice, the whole spectral energy distribution is considered).

The most commonly cited CMB *angular power spectrum* is
of its temperature, but similar spectrums of CMB polarization
and/or gravitational lensing are also used.

(*harmonics,cosmology,CMB,function*)
http://en.wikipedia.org/wiki/Cosmic_microwave_background

**Referenced by:**

CMB lensing

CMB polarization

initial fluctuation spectrum

magnetic field

N-point function

index