  We use a spherical model and an extended excursion set formalism with
drifting diffusive barriers to predict the abundance of cosmic voids in the
context of general relativity as well as f(R) and symmetron models of modified
gravity. We detect spherical voids from a suite of N-body simulations of these
gravity theories and compare the measured void abundance to theory predictions.
We find that our model correctly describes the abundance of both dark matter
and galaxy voids, providing a better fit than previous proposals in the
literature based on static barriers. We use the simulation abundance results to
fit for the abundance model free parameters as a function of modified gravity
parameters, and show that counts of dark matter voids can provide interesting
constraints on modified gravity. For galaxy voids, more closely related to
optical observations, we find that constraining modified gravity from void
abundance alone may be significantly more challenging. In the context of
current and upcoming galaxy surveys, the combination of void and halo
statistics including their abundances, profiles and correlations should be
effective in distinguishing modified gravity models that display different
screening mechanisms.
