Shape invariance method for quintom model in the bent brane background

TL;DR

This paper applies the shape invariance method to analyze the spectrum of metric and quintom field fluctuations in bent brane models with dark energy, providing a new approach to braneworld stability analysis.

Contribution

It introduces the use of shape invariance technique in bent brane scenarios with quintom dark energy, deriving the energy spectrum from first-order formalism.

Findings

Derived the Schrödinger equation for fluctuations

Factorized the Hamiltonian using shape invariance

Obtained the energy spectrum of the system

Abstract

In the present paper, we study the braneworld scenarios in the presence of quintom dark energy coupled by gravity. The first-order formalism for the bent brane (for both de Sitter and anti-de Sitter geometry), leads us to discuss the shape invariance method in the bent brane systems. So, by using the fluctuations of metric and quintom fields we obtain the Schrodinger equation. Then we factorize the corresponding Hamiltonian in terms of multiplication of the first-order differential operators. These first-order operators lead us to obtain the energy spectrum with the help of shape invariance method.