A revised density split statistic model for general filters

¹ Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
e-mail: pburger@astro.uni-bonn.de
² Kavli Institute for Cosmology, University of Cambridge, Cambridge CB3 0HA, UK
³ Churchill College, University of Cambridge, Cambridge CB3 0DS, UK
⁴ School of Mathematics, Statistics and Physics, Newcastle University, Newcastle Upon Tyne NE1 7RU, UK
⁵ Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK

Received: 24 June 2021
Accepted: 2 March 2022

Abstract

Context. Studying the statistical properties of the large-scale structure in the Universe with weak gravitational lensing is a prime goal of several current and forthcoming galaxy surveys. The power that weak lensing has to constrain cosmological parameters can be enhanced by considering statistics beyond second-order shear correlation functions or power spectra. One such higher-order probe that has proven successful in observational data is density split statistics (DSS), in which one analyses the mean shear profiles around points that are classified according to their foreground galaxy density.

Aims. In this paper, we generalise the most accurate DSS model to allow for a broad class of angular filter functions used for the classification of the different local density regions. This approach is motivated by earlier findings showing that an optimised filter can provide tighter constraints on model parameters compared to the standard top-hat case.

Methods. As in the previous DSS model we built on large deviation theory approaches and approximations thereof to model the matter density probability distribution function, and on perturbative calculations of higher-order moments of the density field. The novel addition relies on the generalisation of these previously employed calculations to allow for general filter functions and is validated on several sets of numerical simulations.

Results. It is shown that the revised model fits the simulation measurements well for many filter choices, with a residual systematic offset that is small compared to the statistical accuracy of current weak lensing surveys. However, by use of a simple calibration method and a Markov chain Monte Carlo analysis, we studied the expected sensitivity of the DSS to cosmological parameters and find unbiased results and constraints comparable to the commonly used two-point cosmic shear measures. Hence, our DSS model can be used in competitive analyses of current cosmic shear data, while it may need refinements for forthcoming lensing surveys.