# Constraining phantom braneworld model from cosmic structure sizes

## TL;DR

This paper derives an analytical expression for the maximum size of cosmic structures in the phantom braneworld model and uses observational data to constrain the model's parameters, including the bulk cosmological constant.

## Contribution

It provides the first analytical formula for the maximum turn around radius in the phantom braneworld model and constrains its parameters using real cosmic structure data.

## Key findings

- Predicted upper bounds are larger than observed when the bulk cosmological constant is zero or negative.
- Positive bulk cosmological constant can lead to predicted sizes smaller than observed.
- Constraints on the bulk cosmological constant and model parameters are derived from size observations.

## Abstract

We consider the phantom braneworld model in the context of the maximum turn around radius, $R_{\rm TA,max}$, of a stable, spherical cosmic structure with a given mass. The maximum turn around radius is the point where the attraction due to the central inhomogeneity gets balanced with the repulsion of the ambient dark energy, beyond which a structure cannot hold any mass, thereby giving the maximum upper bound on the size of a stable structure. In this work we derive an analytical expression of $R_{\rm TA,max}$ for this model using cosmological scalar perturbation theory. Using this we numerically constrain the parameter space, including a bulk cosmological constant and the Weyl fluid, from the mass versus observed size data for some nearby, non-virial cosmic structures. We use different values of the matter density parameter $\Omega_m$, both larger and smaller than that of the $\Lambda{\rm CDM}$, as the input in our analysis. We show in particular, that a) with a vanishing bulk cosmological constant the predicted upper bound is always greater than what is actually observed; similar conclusion holds if the bulk cosmological constant is negative b) if it is positive, the predicted maximum size can go considerably below than what is actually observed and owing to the involved nature of the field equations, it leads to interesting constraints on not only the bulk cosmological constant itself but on the whole parameter space of the theory.