Résumé
: 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.
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