# Nonlinear structure formation in Bound Dark Energy

## TL;DR

This paper investigates nonlinear structure formation in the Bound Dark Energy model, revealing that nonlinear effects diminish early differences from standard cosmology but still produce small late-time deviations in matter clustering and halo properties.

## Contribution

It introduces a detailed analysis of nonlinear structure formation in the BDE model, highlighting how nonlinear corrections and halo properties differ from ΛCDM predictions.

## Key findings

- Nonlinear corrections wash out initial matter power spectrum differences.
- A small 2% suppression in BDE matter spectrum at late times.
- Small halos are more abundant in BDE, while large structures are delayed.

## Abstract

We study nonlinear structure formation in the Bound Dark Energy model (BDE), where dark energy (DE) corresponds to a light scalar meson particle $\phi$ dynamically formed at a condensation energy scale $\Lambda_c$. The evolution of this dark-energy meson is determined by the potential $V(\phi)=\Lambda_c^{4+2/3}\phi^{-2/3}$, with a distinguishing phenomenology from other quintessence scenarios. Particularly, the expansion rate of the universe is affected not only at late times, but also when the condensation of $\phi$ occurs, which in linear theory leads to an enhancement (with respect to standard $\Lambda$CDM) of matter perturbations on small scales. We study how much of this signature is still present at late times as well as the properties of dark matter halos in the nonlinear regime through N-body simulations. Our results show that nonlinear corrections wash out this feature from the matter power spectrum even before DE becomes dominant. There is, however, a small but clear suppression of the BDE spectrum of $2\%$ today on the largest scales due to the distinct late-time dynamics of DE. The differences on the clustering power between BDE and $\Lambda$CDM are reflected in the halo mass function, where small halos are more abundant in BDE as opposed to large heavy structures, whose formation is delayed because of the expansion history of the universe. This result is well captured by the semi-analytical Sheth-Tormen formula. However, despite these differences, the halo concentration parameter is essentially the same in both models, which suggest that clustering inside the halos decouple from the general expansion once the halos form.