Large deviation principle at work: Computation of the statistical properties of the exact one-point aperture mass
Résumé
We present a formalism based on the large deviation principle (LDP) applied to cosmological density
fields, and more specifically to the arbitrary functional of density profiles, and we apply it to the derivation
of the cumulant generating function and one-point probability distribution function (PDF) of the aperture
mass ($M_{ap}$), a common observable for cosmic shear observations. We show that the LDP can indeed be
used in practice for a much larger family of observables than previously envisioned, such as those built
from continuous and nonlinear functionals of density profiles. Taking advantage of this formalism, we can
extend previous results, which were based on crude definitions of the aperture mass, with top-hat windows
and the use of the reduced shear approximation (replacing the reduced shear with the shear itself). We were
precisely able to quantify how this latter approximation affects the $M_{ap}$ statistical properties. In particular,
we derive the corrective term for the skewness of the $M_{ap}$ and reconstruct its one-point PDF.
Domaines
Astrophysique [astro-ph]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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