Voids in modified gravity reloaded: Eulerian void assignment

Abstract

We revisit the excursion set approach to calculate void abundances in\nchameleon-type modified gravity theories, which was previously studied by\nClampitt, Cai and Li (2013). We focus on properly accounting for the\nvoid-in-cloud effect, i.e., the growth of those voids sitting in over-dense\nregions may be restricted by the evolution of their surroundings. This effect\nmay change the distribution function of voids hence affect predictions on the\ndifferences between modified gravity and GR. We show that the thin-shell\napproximation usually used to calculate the fifth force is qualitatively good\nbut quantitatively inaccurate. Therefore, it is necessary to numerically solve\nthe fifth force in both over-dense and under-dense regions. We then generalise\nthe Eulerian void assignment method of Paranjape, Lam and Sheth (2012) to our\nmodified gravity model. We implement this method in our Monte Carlo simulations\nand compare its results with the original Lagrangian methods. We find that the\nabundances of small voids are significantly reduced in both modified gravity\nand GR due to the restriction of environments. However, the change in void\nabundances for the range of void radii of interest for both models is similar.\nTherefore, the difference between models remains similar to the results from\nthe Lagrangian method, especially if correlated steps of the random walks are\nused. As Clampitt, Cai and Li (2013), we find that the void abundance is much\nmore sensitive to modified gravity than halo abundances. Our method can then be\na faster alternative to N-body simulations for studying the qualitative\nbehaviour of a broad class of theories. We also discuss the limitations and\nother practical issues associated with its applications.\n