An Extended Excursion Set Approach to Structure Formation in Chameleon Models

TL;DR

This paper extends the excursion set theory to include environmental effects in structure formation, specifically applied to chameleon models, providing a semi-analytical approach to study non-linear cosmic structures.

Contribution

It introduces an extended analytical framework for environmental effects in structure formation, applicable to chameleon and other environmentally dependent models.

Findings

Calculated non-linear mass functions at various redshifts.

Demonstrated the method's applicability to different models.

Provided a tool to identify models needing detailed N-body simulations.

Abstract

In attempts to explain dark energy, a number of models have been proposed in which the formation of large-scale structure depends on the local environment. These models are highly non-linear and difficult to analyse analytically. N-body simulations have therefore been used to study their non-linear evolution. Here we extend excursion set theory to incorporate environmental effects on structure formation. We apply the method to a chameleon model and calculate observables such as the non-linear mass function at various redshifts. The method can be generalized to study other obervables and other models of environmentally dependent interactions. The analytic methods described here should prove useful in delineating which models deserve more detailed study with N-body simulations.