Distinguishing general relativity and $f(R)$ gravity with the gravitational lensing Minkowski functionals

We explore the Minkowski functionals of weak lensing convergence map to distinguish between $f(R)$ gravity and the general relativity (GR). The mock weak lensing convergence maps are constructed with a set of high-resolution simulations assuming different gravity models. It is shown that the lensing MFs of $f(R)$ gravity can be considerably different from that of GR because of the environmentally dependent enhancement of structure formation. We also investigate the effect of lensing noise on our results, and find that it is likely to distinguish F5, F6 and GR gravity models with a galaxy survey of $sim3000$ degree$^2$ and with a background source number density of $n_g=30~{rm arcmin}^{-2}$, comparable to an upcoming survey dark energy survey (DES). We also find that the $f(R)$ signal can be partially degenerate with the effect of changing cosmology, but combined use of other observations, such as the cosmic microwave background (CMB) data, can help break this degeneracy.

Mask Effects on Cosmological Studies with Weak Lensing Peak Statistics

In this paper, we analyze in detail with numerical simulations how the mask effect can influence the weak lensing peak statistics reconstructed from the shear measurement of background galaxies. It is found that high peak fractions are systematically enhanced due to masks, the larger the masked area, the higher the enhancement. In the case with about $13%$ of the total masked area, the fraction of peaks with SNR $ uge 3$ is $sim 11%$ in comparison with $sim 7%$ of the mask-free case in our considered cosmological model. This can induce a large bias on cosmological studies with weak lensing peak statistics. Even for a survey area of $9hbox{ deg}^2$, the bias in $(Omega_m, sigma_8)$ is already close to $3sigma$. It is noted that most of the affected peaks are close to the masked regions. Therefore excluding peaks in those regions can reduce the bias but at the expense of loosing usable survey areas. Further investigations find that the enhancement of high peaks number can be largely attributed to higher noise led by the fewer number of galaxies usable in the reconstruction. Based on Fan et al. (2010), we develop a model in which we exclude only those large masks with radius larger than $3arcmin. For the remained part, we treat the areas close to and away from the masked regions separately with different noise levels. It is shown that this two-noise-level model can account for the mask effect on peak statistics very well and the cosmological bias is significantly reduced.