Proper Fourier decomposition formalism for cosmological fields in spherical shells

Understand

Cosmological random fields are often analysed in spherical Fourier-Bessel basis.

• Compared to the Cartesian Fourier basis this has an advantage of properly taking into account some of the relevant physical processes (redshift-space distortions, redshift evolution).
• The observations usually come in redshift slices and have a partial sky coverage.
• These masking effects strongly correlate Fourier-Bessel modes that are meant for a perfect spherical geometry and result in a lot of redundant measurements.