Constraining f(R) Gravity Theory Using CFHTLenS Weak Lensing Peak Statistics

Fig. Left upper panel: A sketch of Gravitational Lensing. Left lower panel: An example of the reconstructed convergence map from CFHTLenS shear catalog, with white lines represent the corresponding shear patterns. The dark blue regions are the mask regions. The black circles are corresponding to the redMaPPer clusters detected in the field, which shows a good association with weak lensing convergence peaks. Right panel: Peak results (upper) and the derived constraints (lower) for CFHTLenS observational data. Green and red contours are the results with WMAP9 and Planck15 priors, respectively.

The observed cosmic acceleration has posed a great challenge to our understanding about the Universe. It requires either introducing a dark energy component, which possesses an equivalent negative pressure, into the matter content of the Universe, or modifying the general relativity theory of gravity on cosmological scales. The two approaches however, can lead to different structure formation and evolution. Therefore observations of large-scale structures are critical in scrutinizing the underlying mechanism driving the global cosmic acceleration, and thus deepening our view of fundamental physics and cosmology.

Arising from the light deflection by large-scale structures in the Universe, the weak lensing (WL) effect has been recognized as one of the key cosmological probes. With CFHTLenS WL observations (, a team from Peking University, Durham University (UK), National Astronomical Observatories, Chinese Academy of Sciences, and Shanghai Normal University, carried out detailed WL peak analyses and obtained stringent constraints on the Hu-Sawicki f(R) gravity theory.

High peaks in WL maps are closely related to massive halos along lines of sight. Their abundance is therefore sensitive to halo formation and evolution, which in turn is sensitive to the law of gravity. Comparing to cosmological studies using optical, X-ray or Sunyaev-Zeldovich clusters, which rely heavily on baryonic observable–mass relations, WL peak statistics are much less affected by baryonic physics, the major systemic effect concerned in normal cluster studies. On the other hand, WL peak studies have their own systematics. How to predict accurately the cosmological dependence of WL peak abundance is a challenging task. Considering carefully the noise effect arising from intrinsic shapes of source galaxies, the team has developed an analyzing pipe line for cosmological studies using WL high peaks, from theoretical modeling, mock simulation calibrations, to a fast computing platform.


By applying it using CFHTLenS with priors from WMAP and Planck CMB observations, the team has derived tight constraints on the Hu-Sawicki f(R) theory, for the first time, from WL high peak abundance. No deviations from the general relativity theory are detected. The study demonstrates clearly the promising potential of WL peak analyses. With on-going and future large observations with much improved data quantity and quality, we expect WL peak analyses will result in much better cosmological constraints. Low statistical errors in future observations ask for tighter systematic controls in cosmological observables. The team has been continuously working toward fully realizing the power of WL analyses in future cosmological studies.


Published paper:

Liu, Xiangkun; Li, Baojiu; Zhao, Gong-Bo; Chiu, Mu-Chen; Fang, Wei; Pan, Chuzhong; Wang, Qiao; Du, Wei; Yuan, Shuo; Fu, Liping; Fan, Zuhui, 2016,  Physical Review Letters, 117, 051101 (arXiv: 1607.00184),“Constraining f(R) Gravity Theory Using Weak Lensing Peak Statistics from the Canada-France-Hawaii-Telescope Lensing Survey”