Constraining $f(R)$ Gravity Theory Using Weak Lensing Peak Statistics from the Canada-France-Hawaii-Telescope Lensing Survey

In this Letter, we report the observational constraints on the Hu-Sawicki $f(R)$ theory derived from weak lensing peak abundances, which are closely related to the mass function of massive halos. In comparison with studies using optical or x-ray clusters of galaxies, weak lensing peak analyses have the advantages of not relying on mass-baryonic observable calibrations. With observations from the Canada-France-Hawaii-Telescope Lensing Survey, our peak analyses give rise to a tight constraint on the model parameter $|f_{R0}|$ for $n=1$. The 95% C.L. is ${\log }_{10}|f_{R0}|<-4.82$ given WMAP9 priors on (${\mathrm{\Omega }}_m$, $A_s$). With Planck15 priors, the corresponding result is ${\log }_{10}|f_{R0}|<-5.16$.

Figure 1

Peak counts distribution from $F5$ (upper left) and GR (upper right) mock simulations. Different symbols with different colors correspond to different noise realizations. The blue asterisk (*) and the error bars are for the average values and the rms over the 15 realizations. The solid line is for our model predictions. The lower panel is for the difference ratios.

Figure 2

Constraints derived from $F5$ (upper) and GR (lower) mock data. In 1D distributions, blue solid and dashed lines indicate the locations of the maximum marginalized probabilities, and the corresponding 68% confidence intervals. Red solid lines and plus ($+$) symbols are the input parameters of the mock simulations. For the GR case, $f_{R0}=0$, and we only indicate the input ${\mathrm{\Omega }}_m$ and ${\sigma }_8$.

Figure 3

Results from CFHTLenS observational data. Left: The peak counts distribution. The corresponding solid lines are the theoretical predictions with the best-fit cosmological parameters listed therein. The error bars are the square root of the diagonal terms of the covariance matrix. Right: The derived constraints. Green and red contours are the results with WMAP9 and Planck15 priors, respectively.