Instability of de Sitter brane and horizon entropy in a 6D braneworld

TL;DR

This paper studies the stability of six-dimensional de Sitter braneworld solutions, revealing a correlation between thermodynamic and dynamical instabilities, with high expansion rates leading to tachyonic modes and instability.

Contribution

It demonstrates a direct link between thermodynamic and dynamical stability in 6D braneworld models, highlighting the role of entropy and perturbation analysis.

Findings

High-entropy branch is thermodynamically stable

Low-entropy branch is thermodynamically unstable

Large Hubble rates induce scalar tachyonic modes

Abstract

We investigate thermodynamic and dynamical stability of a family of six-dimensional braneworld solutions with de Sitter branes. First, we investigate thermodynamic stability in terms of de Sitter entropy. We see that the family of solutions is divided into two distinct branches: the high-entropy branch and the low-entropy branch. By analogy with ordinary thermodynamics, the high-entropy branch is expected to be stable and the low-entropy branch to be unstable. Next, we investigate dynamical stability by analyzing linear perturbations around the solutions. Perturbations are decomposed into scalar, vector and tensor sectors according to the representation of the 4D de Sitter symmetry, and each sector is analyzed separately. It is found that when the Hubble expansion rates on the branes are too large, there appears a tachyonic mode in the scalar sector and the background solution becomes dynamically unstable. We show analytically that the onset of the thermodynamic instability and that of the dynamical instability exactly coincide. Therefore, the braneworld model provides a new example illustrating close relations between thermodynamic and dynamical instability.