The impact of super-survey modes on cosmological constraints from cosmic
  shear fields
  Owing to the mass-sheet degeneracy, cosmic shear maps do not probe directly
the Fourier modes of the underlying mass distribution on scales comparable to
the survey size and larger. To assess the corresponding effect on attainable
cosmological parameter constraints, we quantify the information on super-survey
modes in a lognormal model and, when interpreted as nuisance parameters, their
degeneracies to cosmological parameters. Our analytical and numerical
calculations clarify the central role of super-sample covariance (SSC) in
shaping the statistical power of cosmological observables. Reconstructing the
background modes from their non-Gaussian statistical dependence to small scales
modes yields the renormalized convergence. This diagonalizes the spectrum
covariance matrix, and the information content of the corresponding power
spectrum is increased by a factor of two over standard methods. Unfortunately,
careful calculation of the Cramer-Rao bound shows that the information recovery
can never be made complete, any observable built from shear fields, including
optimal sufficient statistics, are subject to severe information loss,
typically $80\%$ to $90\%$ below $\ell \sim 3000$ for generic cosmological
parameters. The lost information can only be recovered from additional,
non-shear based data. Our predictions hold just as well for a tomographic
analysis, and/or full sky surveys.
