The imprint of $f(R)$ gravity on weak gravitational lensing II : Information content in cosmic shear statistics

We investigate the information content of various cosmic shear statistics on the theory of gravity. Focusing on the Hu-Sawicki-type $f(R)$ model, we perform a set of ray-tracing simulations and measure the convergence bispectrum, peak counts and Minkowski functionals. We first show that while the convergence power spectrum does have sensitivity to the current value of extra scalar degree of freedom $|f_{\rm R0}|$, it is largely compensated by a change in the present density amplitude parameter $\sigma_{8}$ and the matter density parameter $\Omega_{\rm m0}$. With accurate covariance matrices obtained from 1000 lensing simulations, we then examine the constraining power of the three additional statistics. We find that these probes are indeed helpful to break the parameter degeneracy, which can not be resolved from the power spectrum alone. We show that especially the peak counts and Minkowski functionals have the potential to rigorously (marginally) detect the signature of modified gravity with the parameter $|f_{\rm R0}|$ as small as $10^{-5}$ ($10^{-6}$) if we can properly model them on small ($\sim 1\, \mathrm{arcmin}$) scale in a future survey with a sky coverage of 1,500 squared degrees. We also show that the signal level is similar among the additional three statistics and all of them provide complementary information to the power spectrum. These findings indicate the importance of combining multiple probes beyond the standard power spectrum analysis to detect possible modifications to General Relativity.