  The weak lensing power spectrum carries cosmological information via its
dependence on the growth of structure and on geometric factors. Since much of
the cosmological information comes from scales affected by nonlinear
clustering, measurements of the lensing power spectrum can be degraded by
non-Gaussian covariances. Recently there have been conflicting studies about
the level of this degradation. We use the halo model to estimate it and include
new contributions related to the finite size of lensing surveys, following
Rimes and Hamilton's study of 3D simulations. We find that non-Gaussian
correlations between different multipoles can degrade the cumulative
signal-to-noise for the power spectrum amplitude by up to a factor of 2 (or 5
for a worst-case model that exceeds current N-body simulation predictions).
However, using an eight-parameter Fisher analysis we find that the marginalized
errors on individual parameters are degraded by less than 10% (or 20% for the
worst-case model). The smaller degradation in parameter accuracy is primarily
because: individual parameters in a high-dimensional parameter space are
degraded much less than the volume of the full Fisher ellipsoid; lensing
involves projections along the line of sight, which reduce the non-Gaussian
effect; some of the cosmological information comes from geometric factors which
are not degraded at all. We contrast our findings with those of Lee & Pen
(2008) who suggested a much larger degradation in information content. Finally,
our results give a useful guide for exploring survey design by giving the
cosmological information returns for varying survey area, depth and the level
of some systematic errors.
