Cosmological information in Gaussianised weak lensing signals
  We investigate the information on cosmology contained in Gaussianised weak
gravitational lensing convergence fields. Employing Box-Cox transformations to
determine optimal transformations to Gaussianity, we develop analytical models
for the transformed power spectrum, including effects of noise and smoothing.
We find that optimised Box-Cox transformations perform substantially better
than an offset logarithmic transformation in Gaussianising the convergence, but
both yield very similar results for the signal-to-noise and parameter
constraints. None of the transformations is capable of eliminating correlations
of the power spectra between different angular frequencies, which we
demonstrate to have a significant impact on the errors on cosmology. Analytic
models of the Gaussianised power spectrum yield good fits to the simulations
and produce unbiased parameter estimates in the majority of cases, where the
exceptions can be traced back to the limitations in modelling the higher-order
correlations of the original convergence. In the idealistic case, without
galaxy shape noise, we find an increase in cumulative signal-to-noise by a
factor of 2.6 for angular frequencies up to 1500, and a decrease in the area of
the confidence region in the Omega_m-sigma_8 plane by a factor of 4.4 in terms
of q-values for the best-performing transformation. When adding a realistic
level of shape noise, all transformations perform poorly with little
decorrelation of angular frequencies, a maximum increase in signal-to-noise of
34%, and even marginally degraded errors on cosmological parameters. We argue
that, to find Gaussianising transformations of practical use, one will need to
go beyond transformations of the one-point distribution of the convergence,
extend the analysis deeper into the non-linear regime, and resort to an
exploration of parameter space via simulations. (abridged)
