# Cosmic structure sizes in generic dark energy models

## TL;DR

This paper investigates the maximum sizes of cosmic structures in various dark energy models, deriving new theoretical results and constraining dark energy parameters using observational data.

## Contribution

It extends the calculation of maximum structure sizes to non-$w=-1$ models, incorporates dark energy inhomogeneities, and tests specific dark energy models against observations.

## Key findings

- Derived $R_{TA,max}$ using static geometry for $w
eq -1$
- Constrained $w(t=\text{today}) > -2.3$ from data
- Quintessence and Chaplygin gas models predict consistent structure sizes

## Abstract

The maximum allowable size of a spherical cosmic structure as a function of its mass is determined by the maximum turn around radius $R_{\rm TA,max}$, the distance from its centre where the attraction on a radial test particle due to the spherical mass is balanced with the repulsion due to the ambient dark energy. In this work, we extend the existing results in several directions. (a) We first show that for $w\neq -1$, the expression for $R_{\rm TA, max}$ found earlier using the cosmological perturbation theory, can be derived using a static geometry as well. (b) In the generic dark energy model with arbitrary time dependent state parameter $w(t)$, taking into account the effect of inhomogeneities upon the dark energy as well, where it is shown that the data constrain $w(t={\rm today})>-2.3$, and (c) in the quintessence and the generalized Chaplygin gas models, both of which are shown to predict structure sizes consistent with observations.