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

Understand

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).