Excursion set theory for modified gravity: Eulerian versus Lagrangian environments

TL;DR

This paper revisits the excursion set theory in modified gravity, comparing Eulerian and Lagrangian environments, revealing differences in environmental density distributions and implications for matter clustering and halo formation.

Contribution

It introduces the use of Eulerian environments in the extended excursion set theory for modified gravity, addressing limitations of Lagrangian environments.

Findings

Eulerian environments have higher matter density probabilities.

Using Eulerian environments avoids unphysical mass limits.

Numerical integration and Monte Carlo methods yield consistent results.

Abstract

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