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

TL;DR

This study demonstrates that Minkowski functionals of weak lensing maps can effectively differentiate between $f(R)$ gravity and general relativity, even with observational noise, aiding in testing gravity theories with upcoming surveys.

Contribution

The paper introduces a method using Minkowski functionals of weak lensing maps from simulations to distinguish $f(R)$ gravity from GR, accounting for observational noise and degeneracies.

Findings

Minkowski functionals differ significantly between $f(R)$ and GR models.

Upcoming galaxy surveys can potentially distinguish these gravity models.

Combining lensing data with CMB observations helps resolve degeneracies.

Abstract

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.