Disconnected pseudo-$C_\ell$ covariances for projected large-scale structure data

Understand

The disconnected part of the power spectrum covariance matrix (also known as the "Gaussian" covariance) is the dominant contribution on large scales for galaxy clustering and weak lensing datasets.

• The presence of a complicated sky mask causes non-trivial correlations between different Fourier/harmonic modes, which must be accurately characterized in order to obtain reliable cosmological constraints.
• This is particularly relevant for galaxy survey data.
• Unfortunately, an exact calculation of these correlations involves $O(\ell_{\rm max}^6)$ operations that become computationally impractical very quickly.