Forecasting Constraints on the Evolution of the Hubble Parameter and the Growth Function by Future Weak Lensing Surveys

Abstract: The cosmological information encapsulated within a weak lensing signal can be accessed via the power spectrum of the so called convergence. We use the Fisher information matrix formalism with the convergence power spectrum as the observable to predict how future weak lensing surveys will constrain the expansion rate and the growth function as functions of redshift without using any specific model to parameterize these two quantities. To do this, we divide redshift space into bins and linearly interpolate the functions with the centers of the redshift bins as sampling points, using a fiducial set of parameters. At the same time, we use these redshift bins for power spectrum tomography, where we analyze not only the power spectrum in each bin but also their cross-correlation in order to maximize the extracted information. We find that a small number of bins with the given photometric redshift mea- surement precision is sufficient to access most of the information content and that the projected constraints are comparable to current constraints from X-ray cluster growth data. This way, the weak lensing data alone might be able to rule out some modified gravity theories only at the 2{\sigma} level, but when including priors from surveys of the cosmic microwave background radiation this would improve to a 3{\sigma} level.