Cuscuton kinks and branes

TL;DR

This paper explores a modified scalar field model with a cuscuton term, analyzing kink solutions, energy properties, stability, and braneworld implications, revealing how the cuscuton influences the system's behavior and stability.

Contribution

It introduces a novel scalar field model with a cuscuton term, deriving first order equations, energy characteristics, and stability analysis, including applications to braneworld scenarios.

Findings

Modified kink solutions due to the cuscuton term

Stable linear perturbations governed by a Schrödinger-like equation

Successful extension of the model to braneworld scenarios

Abstract

In this paper, we study a peculiar model for the scalar field. We add the cuscuton term in a standard model and investigate how this inclusion modifies the usual behavior of kinks. We find the first order equations and calculate the energy density and the total energy of the system. Also, we investigate the linear stability of the model, which is governed by a Sturm-Liouville eigenvalue equation that can be transformed in an equation of the Shcr\"odinger type. The model is also investigated in the braneworld scenario, where a first order formalism is also obtained and the linear stability is investigated.