Tomography from the next generation of cosmic shear experiments for viable f(R) models

We present the cosmic shear signal predicted by two viable cosmological models in the framework of modified-action f(R) theories. We use f (R) models where the current accelerated expansion of the Universe is a direct consequence of the modified gravitational Lagrangian rather than Dark Energy (DE), either in the form of vacuum energy/cosmological constant or of a dynamical scalar field (e.g. quintessence). We choose Starobinsky's (St) and Hu & Sawicki's (HS) f(R) models, which are carefully designed to pass the Solar System gravity tests. In order to further support - or rule out - f(R) theories as alternative candidates to the DE hypothesis, we exploit the power of weak gravitational lensing, specifically of cosmic shear. We calculate the tomographic shear matrix as it would be measured by the upcoming ESA Cosmic Vision Euclid satellite. We find that in the St model the cosmic shear signal is almost completely degenerate with Lambda CDM but it is easily distinguishable in the HS model. Moreover, we compute the corresponding Fisher matrix for both the St and LIS models, thus obtaining forecasts for their cosmological parameters. Finally, we show that the Bayes factor for cosmic shear will definitely favour the HS model over Lambda CDM if Euclid measures a value larger than similar to 0.02 for the extra HS parameter n(HS).