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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.


Referenced by:
CMB lensing
CMB polarization
initial fluctuation spectrum
magnetic field
N-point function