Excursion set theory for modified gravity: Eulerian versus Lagrangian environments

Abstract

We have revisited the extended excursion set theory in modified gravity\nmodels, taking the chameleon model as an example. Instead of specifying their\nLagrangian size, here we define the environments by the Eulerian size, chosen\nto be of the same order of the Compton length of the scalar field by physical\narguments. We find that the Eulerian and Lagrangian environments have very\ndifferent environmental density contrast probability distributions, the former\nmore likely to have high matter density, which in turn suppressing the effect\nof the fifth force in matter clustering and halo formation. The use of Eulerian\nenvironments also evades the unphysical restriction of having an upper mass\nlimit in the case of Lagrangian environments.Two methods of computing the\nunconditional mass functions, numerical integration and Monte Carlo simulation,\nare discussed and found to give consistent predictions.\n