Voids in Modified Gravity: Excursion Set Predictions
  We investigate the behavior of the fifth force in voids in chameleon models using the spherical collapse method. Contrary to Newtonian gravity, we find the fifth force is repulsive in voids. The strength of the fifth force depends on the density inside and outside the void region as well as its radius. It can be many times larger than the Newtonian force and their ratio is in principle unbound. This is very different from the case in halos, where the fifth force is no more than 1/3 of gravity. The evolution of voids is governed by the Newtonian gravity, the effective dark energy force and the fifth force. While the first two forces are common in both LCDM and chameleon universes, the fifth force is unique to the latter. Driven by the outward-pointing fifth force, individual voids in chameleon models expand faster and grow larger than in a LCDM universe. The expansion velocity of the void shell can be 20% to 30% larger for voids of a few Mpc/h in radius, while their sizes can be larger by ~10%. These differences are smaller for larger voids of the same density. We compare void statistics using excursion set theory; for voids of the same size, their number density is larger in chameleon models. The fractional difference increases with void size. The chance of having voids of radius ~25 Mpc/h can be 2.5 times larger. This difference is about 10 times larger than that in the halo mass function. We find strong environmental dependence of void properties in chameleon models. The differences in size and expansion velocity with GR are both larger for small voids in high density regions. In general, the difference between chameleon models and LCDM in void properties (size, expansion velocity and distribution function) are larger than the corresponding quantities for halos. This suggests that voids might be better candidates than halos for testing gravity. 
Joseph Clampitt (UPenn), Yan-Chuan Cai (Durham), Baojiu Li (Durham)
astro-ph.CO