Cosmic Shear Tomography and Efficient Data Compression using COSEBIs
  Context. Gravitational lensing is one of the leading tools in understanding
the dark side of the Universe. The need for accurate, efficient and effective
methods which are able to extract this information along with other
cosmological parameters from cosmic shear data is ever growing. COSEBIs,
Complete Orthogonal Sets of E-/B-Integrals, is a recently developed statistical
measure that encompasses the complete E-/B-mode separable information contained
in the shear correlation functions measured on a finite angular range. Aims.
The aim of the present work is to test the properties of this newly developed
statistics for a higher-dimensional parameter space and to generalize and test
it for shear tomography. Methods. We use Fisher analysis to study the
effectiveness of COSEBIs. We show our results in terms of figure-of-merit
quantities, based on Fisher matrices. Results. We find that a relatively small
number of COSEBIs modes is always enough to saturate to the maximum information
level. This number is always smaller for 'logarithmic COSEBIs' than for 'linear
COSEBIs', and also depends on the number of redshift bins, the number and
choice of cosmological parameters, as well as the survey characteristics.
Conclusions. COSEBIs provide a very compact way of analyzing cosmic shear data,
i.e., all the E-/B-mode separable second-order statistical information in the
data is reduced to a small number of COSEBIs modes. Furthermore, with this
method the arbitrariness in data binning is no longer an issue since the
COSEBIs modes are discrete. Finally, the small number of modes also implies
that covariances, and their inverse, are much more conveniently obtainable,
e.g., from numerical simulations, than for the shear correlation functions
themselves.
