Recovery of fluctuation spectrum evolution from tomographic shear spectra

Forthcoming large angle surveys are planned to obtain high precision tomographic shear data. In principle, they will allow us to recover the spectra of matter density fluctuation, at various redshift, through the inversion of the expressions yielding shear spectra from fluctuation spectra. This was discussed in previous work, where SVD techniques for matrix inversion were also shown to be the optimal tool to this aim. Here we show the significant improvements obtainable by using a 7 bin tomography, as allowed by future Euclid data, and discuss error propagation from shear to fluctuation spectra. We find that the technique is a promising tool, namely for the analysis of baryon physics through high–` shear spectra and to test the consistency between expansion rate and fluctuation growth.