An equation of state for purely kinetic k-essence inspired by cosmic topological defects

TL;DR

This paper explores a purely kinetic k-essence model inspired by superconducting membranes, analyzing its physical properties, evolution, and compatibility with cosmological observations like luminosity distance and the Alcock-Paczyński test.

Contribution

It introduces a novel kinetic k-essence model based on topological defect physics and constrains its parameters using cosmological data and stability criteria.

Findings

The model's equation of state parameter $w$ varies with redshift.

Parameter restrictions ensure physically acceptable behavior.

The luminosity distance evolution aligns with observational data.

Abstract

We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter $w$ and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. Furthermore, we analyze the evolution of the luminosity distance $d_{L}$ with redshift $z$ by comparing (normalizing) it with the $\Lambda$CDM model. Since the equation of state parameter is $z$-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczy\'{n}ski test.