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We study how well the Gaussian approximation is valid for computing thecovariance matrices of the convergence power and bispectrum in weakgravitational lensing analyses. We focus on its impact on the cosmologicalparameter estimations by comparing the results with and without non-Gaussianerror contribution in the covariance matrix. We numerically derive thecovariance matrix as well as the cosmology dependence of the spectra from alarge set of N-body simulations performed for various cosmologies and carry outFisher matrix forecasts for tomographic weak lensing surveys with three sourceredshifts. After showing the consistency of the power and bispectra measuredfrom our simulations with the state-of-the-art fitting formulas, we investigatethe covariance matrix assuming a typical ongoing survey across 1500 deg^2 withthe mean source number density of 30 arcmin^{-2} at the mean redshift z_s=1.0.Although the shape noise contributes a significant fraction to the total errorbudget and it mitigates the impact of the non-Gaussian error for this sourcenumber density, we find that the non-Gaussian error degrades the cumulativesignal-to-noise ratio up to the maximum multipole of 2000 by a factor of about2 (3) in the power (bi-) spectrum analysis. Its impact on the finalcosmological parameter forecast with 6 parameters can be as large as 15% in thesize of the one-dimensional statistical error. This can be a problem in futurewide and deep weak lensing surveys for precision cosmology. We also show howmuch the dark energy figure of merit is affected by the non-Gaussian errorcontribution and demonstrate an optimal survey design with a fixedobservational time.

Impact of the non-Gaussian covariance of the weak lensing power spectrum and bispectrum on cosmological parameter estimation