title: Information escaping the correlation hierarchy of the convergence field in the study of cosmological parameters.
abstract: Using fits to numerical simulations, we show that the entire hierarchy of moments quickly ceases to provide a complete description of the convergence one-point probability density function leaving the linear regime. This suggests that the full N-point correlation function hierarchy of the convergence field becomes quickly generically incomplete and a very poor cosmological probe on nonlinear scales. At the scale of unit variance, only 5% of the Fisher information content of the one-point probability density function is still contained in its hierarchy of moments, making clear that information escaping the hierarchy is a far stronger effect than information propagating to higher order moments. It follows that the constraints on cosmological parameters achievable through extraction of the entire hierarchy become suboptimal by large amounts. A simple logarithmic mapping makes the moment hierarchy well suited again for parameter extraction.
authors.affiliation: Institute for Astronomy, ETHZ, Zurich, Switzerland. jcarron@phys.ethz.ch
authors.forename: Julien
authors.initials: J
authors.lastname: Carron