Radially symmetric scalar field solutions in the presence of cuscuton term

TL;DR

This paper explores radially symmetric scalar field solutions with a cuscuton term, establishing a first-order formalism that ensures stable, minimum-energy configurations without instabilities across various models.

Contribution

It introduces a novel first-order formalism for scalar fields with cuscuton terms, demonstrating stability and providing analytical solutions in multiple models.

Findings

Cuscuton term does not cause instabilities in solutions

First-order formalism supports minimum energy configurations

Analytical solutions and energy densities are derived for specific models

Abstract

In this work, we investigate radially symmetric solutions in arbitrary dimensions in scalar field models in the presence of the cuscuton term. We introduce a first-order formalism compatible with the equation of motion which supports field configurations engendering minimum energy and show that the cuscuton term does not induce instabilities in the solutions. To illustrate the general results, we study two distinct classes of models and present analytical solutions and the corresponding energy densities.