First step toward matter power spectrum reconstruction with Stage III weak gravitational lensing surveys

Weak gravitational lensing (WL) surveys provide insight into the matter distribution over an extensive range of scales. Current WL results are in mild tension with cosmic microwave background measurements from the early Universe. Reconstructing the matter power spectrum from their measurements instead of condensing the information into a single cosmological parameter may help locate the origin of these differences. To investigate the cosmic shear measurements of Stage III WL surveys, we compared their tomographic data by assuming a simple parametric model for the matter power spectrum. The model allows the comparison of surveys with different characteristics and, in an agnostic approach, gives insight into the shape of the matter power spectrum preferred by the data. For the matter power spectrum, we assumed a double power-law model in scale factor and wavenumber. The best-fitting amplitude and exponents were inferred in an MCMC analysis. We identified the scales to which the data is most sensitive. We tested the sensitivity to different assumptions of the intrinsic alignment strength. We find that the constraining power of Stage III surveys on the power spectrum shape and evolution is still limited. Most information can be summarized as an overall amplitude at a pivot point in wavenumber and scale factor, while constraints on the power-law indices are considerably weaker. Nevertheless, all surveys show a weaker rate of growth from $z=$ 0.5 to 0.1 than predicted. The assumed intrinsic alignment strength is found to have no significant impact on the measured parameters and goodness of fit. Direct estimates of the matter power spectrum from Stage III weak lensing surveys can, in principle, be used to locate the physical origin of the observed $S_8$ tension. We present a simple methodology for the first steps in this direction, but find that current constraints are still weak.