Direct recovery of fluctuation spectra from tomographic shear spectra

Forthcoming experiments will enable us to determine high precision tomographic shear spectra. Matter density fluctuation spectra, at various z, should then be recovered from 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