Non-Gaussian likelihood of weak lensing power spectra

The power spectrum of weak lensing fluctuations has a non-Gaussian distribution due to its quadratic nature. On small scales the Central Limit Theorem acts Gaussianize this but non-Gaussianity in signal gravitational collapse is increasing and functional form likelihood unclear. Analyses have traditionally assumed Gaussian with non-linearity incorporated into covariance matrix; here we provide theory underpinning assumption. We calculate, for first time, leading-order correction angular spectra from underlying study transition Gaussianity. Our expressions are valid an arbitrary number correlated maps correct Wishart presence (but otherwise arbitrary) signal. Surprisingly, resulting not equivalent Edgeworth expansion. effect broaden matrix by usual trispectrum term, residual skewness sourced square bispectrum. Using lognormal demonstrate that our uniquely able model both large mildly non-linear scales. easy-to-compute statistics quantify size corrections. show full can be accurately modelled as on small, imparts negligible likelihood, which takes full-sky case. formalism equally applicable any kind projected field.