We explore voids in dark matter and halo fields from simulations of Λ cold dark matter and Hu-Sawicki f(R) models. In f(R) gravity, dark matter void abundances are greater than that of general relativity (GR). Differences for halo void abundances are much smaller, but still at the 2σ, 6σ and 14σ level for the f(R) model parameter |f<inf>R0</inf>| = 10<sup>-6</sup>, 10<sup>-5</sup> and 10<sup>-4</sup>. Counter-intuitively, the abundance of large voids found using haloes in f(R) gravity is lower, which suggests that voids are not necessarily emptier of galaxies in this model. We find the halo number density profiles of voids are not distinguishable from GR, but the same voids are emptier of dark matter in f(R) gravity. This can be observed by weak gravitational lensing of voids, for which the combination of a spec-z and a photo-z survey over the same sky is necessary. For a volume of 1 (Gpc h<sup>-1</sup>)<sup>3</sup>, |f<inf>R0</inf>| = 10<sup>-5</sup> and 10<sup>-4</sup> may be distinguished from GR at 4σ and 8σ using the lensing tangential shear signal around voids. Sample variance and line-of-sight projection effect sets limits for constraining |f<inf>R0</inf>| = 10<sup>-6</sup>. This might be overcome with a larger volume. The smaller halo void abundance and the stronger lensing shear signal of voids in f(R) models may be combined to break the degeneracy between |f<inf>R0</inf>| and σ<inf>8</inf>. The outflow of dark matter from void centres are 5, 15 and 35 per cent faster in f(R) gravity for |f<inf>R0</inf>| = 10<sup>-6</sup>, 10<sup>-5</sup> and 10<sup>-4</sup>. The velocity dispersions are greater than that in GR by similar amounts. Model differences in velocities imply potential powerful constraints for the model in phase space and in redshift space.
- Gravitational lensing: weak
- Large-scale structure of universe
- Methods: statistical