Probing cosmology with weak lensing selected clusters II: Dark energy and f(R) gravity models

Ongoing and future wide-field galaxy surveys can be used to locate a number of clusters of galaxies with cosmic shear measurement alone. We study constraints on cosmological models using statistics of weak lensing selected galaxy clusters. We extend our previous theoretical framework to model the statistical properties of clusters in variants of cosmological models as well as in the standard $\Lambda$CDM model. Weak lensing selection of clusters does not rely on the conventional assumption such as the relation between luminosity and mass and/or hydrostatic equilibrium, but a number of observational effects compromise robust identification. We use a large set of realistic mock weak-lensing catalogs as well as analytic models to perform a Fisher analysis and make forecast for constraining two competing cosmological models, $w$CDM model and $f(R)$ model proposed by Hu & Sawicki, with our lensing statistics. We show that weak lensing selected clusters are excellent probe of cosmology when combined with cosmic shear power spectrum even in presence of galaxy shape noise and masked regions. With the information of weak lensing selected clusters, the precision of cosmological parameter estimate can be improved by a factor of $\sim1.6$ and $\sim8$ for $w$CDM model and $f(R)$ model, respectively. Hyper Suprime-Cam survey with sky coverage of $1250$ squared degrees can constrain the equation of state of dark energy $w_{0}$ with a level of $\Delta w_0 \sim0.1$. It can also constrain the additional scalar degree of freedom in $f(R)$ model with a level of $|f_{R0}| \sim5\times10^{-6}$, when constraints from cosmic microwave background measurements are incorporated. Future weak lensing surveys with sky coverage of $20,000$ squared degrees will place tighter constraints on $w_{0}$ and $|f_{R0}|$ even without cosmic microwave background measurements.