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We investigate whether a Gaussian likelihood is sufficient to obtain accurateparameter constraints from a Euclid-like combined tomographic power spectrumanalysis of weak lensing, galaxy clustering and their cross-correlation.Testing its performance on the full sky against the Wishart distribution, whichis the exact likelihood under the assumption of Gaussian fields, we find thatthe Gaussian likelihood returns accurate parameter constraints. This accuracyis robust to the choices made in the likelihood analysis, including the choiceof fiducial cosmology, the range of scales included, and the random noiselevel. We extend our results to the cut sky by evaluating the additionalnon-Gaussianity of the joint cut-sky likelihood in both its marginaldistributions and dependence structure. We find that the cut-sky likelihood ismore non-Gaussian than the full-sky likelihood, but at a level insufficient tointroduce significant inaccuracy into parameter constraints obtained using theGaussian likelihood. Our results should not be affected by the assumption ofGaussian fields, as this approximation only becomes inaccurate on small scales,which in turn corresponds to the limit in which any non-Gaussianity of thelikelihood becomes negligible. We nevertheless compare against N-body weaklensing simulations and find no evidence of significant additionalnon-Gaussianity in the likelihood. Our results indicate that a Gaussianlikelihood will be sufficient for robust parameter constraints with powerspectra from Stage IV weak lensing surveys.

Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys