Astronomy and Astrophysics – Astrophysics – Instrumentation and Methods for Astrophysics
Scientific paper
2012-01-04
Phys.Rev.Lett.108:071301,2012
Astronomy and Astrophysics
Astrophysics
Instrumentation and Methods for Astrophysics
Matches version published in PRL. Only minor changes w.r.t. v1
Scientific paper
10.1103/PhysRevLett.108.071301
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.
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