Testing modified gravity with cosmic shear

We use the cosmic shear data from the Canada–France–Hawaii Telescope Lensing Survey to place constraints on f(R) and Generalized Dilaton models of modified gravity. This is highly complementary to other probes since the constraints mainly come from the non-linear scales: maximal deviations with respects to the General Relativity (GR) + Λ cold dark matter (ΛCDM) scenario occurs at k ∼ 1 h Mpc−1. At these scales, it becomes necessary to account for known degeneracies with baryon feedback and massive neutrinos, hence we place constraints jointly on these three physical effects. To achieve this, we formulate these modified gravity theories within a common tomographic parametrization, we compute their impact on the clustering properties relative to a GR universe, and propagate the observed modifications into the weak lensing ξ± quantity. Confronted against the cosmic shear data, we reject the f(R) $\lbrace |f_{R_0}| = 10^{-4}, n = 1\rbrace$ model with more than 99.9 per cent confidence interval (CI) when assuming a ΛCDM dark matter only model. In the presence of baryonic feedback processes and massive neutrinos with total mass up to 0.2 eV, the model is disfavoured with at least 94 per cent CI in all different combinations studied. Constraints on the $\lbrace |f_{R_0}| = 10^{-4}, n = 2\rbrace$ model are weaker, but nevertheless disfavoured with at least 89 per cent CI. We identify several specific combinations of neutrino mass, baryon feedback and f(R) or Dilaton gravity models that are excluded by the current cosmic shear data. Notably, universes with three massless neutrinos and no baryon feedback are strongly disfavoured in all modified gravity scenarios studied. These results indicate that competitive constraints may be achieved with future cosmic shear data.