Working out density fluctuation spectra from shear spectra

TL;DR

This paper develops a method to derive matter density fluctuation spectra from observed shear spectra using SVD matrix inversion, aiding cosmological model constraints.

Contribution

It introduces the inverse analytical expression to extract density fluctuation spectra from shear spectra, complementing existing methods.

Findings

Successfully demonstrates the inverse method with examples

Provides detailed procedure for matrix inversion using SVD

Enables direct extraction of fluctuation spectra from observational data

Abstract

Forthcoming experiments will enable us to determine high precision tomographic shear spectra. Matter density fluctuation spectra, at various $z$, should then be worked out of them, in order to constrain the model and determine the DE state equation. Available analytical expressions, however, do the opposite, enabling us to derive shear spectra from fluctuation spectra. Here we find the inverse expression, yielding density fluctuation spectra from observational tomographic shear spectra. The procedure involves SVD techniques for matrix inversion. We show in detail how the approach works and provide a few examples.