# Large deviations theory approach to cosmic shear calculations: the one-point aperture mass

Abstract : This paper presents a general formalism that allows the derivation of the cumulant generating function and one-point Probability Distribution Function (PDF) of the aperture mass ($\hat M$_{ap}), a common observable for cosmic shear observations. Our formalism is based on the Large Deviation Principle (LDP) applied, in such cosmological context, to an arbitrary set of densities in concentric cells. We show here that the LDP can indeed be used for a much larger family of observables than previously envisioned, such as those built from continuous and nonlinear functionals of the density profiles. The general expression of the observable aperture mass depends on reduced shear profile making it a rather involved function of the projected density field. Because of this difficulty, an approximation that is commonly employed consists in replacing the reduced shear by the shear in such a construction neglecting therefore non-linear effects. We were precisely able to quantify how this approximation affects the \hat M$_{ap}$ statistical properties. In particular we derive the corrective term for the skewness of the $\hat M$$_{ap}$ and reconstruct its one-point PDF.
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [16 references]

https://hal-cea.archives-ouvertes.fr/cea-01677116
Contributor : Emmanuelle De Laborderie Connect in order to contact the contributor
Submitted on : Monday, January 8, 2018 - 9:42:48 AM
Last modification on : Tuesday, January 4, 2022 - 3:44:08 AM
Long-term archiving on: : Wednesday, May 23, 2018 - 2:46:38 PM

### File

1708.00252.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : cea-01677116, version 1

### Citation

Paulo Reimberg, Francis Bernardeau. Large deviations theory approach to cosmic shear calculations: the one-point aperture mass. 2018. ⟨cea-01677116⟩

Record views