Thermodynamic and dynamical stability of Freund-Rubin compactification

TL;DR

This paper examines the thermodynamic and dynamical stability of Freund-Rubin compactifications, including warped solutions, showing their stability properties are consistent and discussing implications for cosmology.

Contribution

It provides a comprehensive analysis of both thermodynamic and dynamical stability of multiple Freund-Rubin solutions, including warped geometries, and interprets results in a cosmological context.

Findings

Thermodynamic and dynamical stabilities are in complete agreement.

Warped solutions can be stable or unstable depending on parameters.

Results have implications for cosmological models involving extra dimensions.

Abstract

We investigate stability of two branches of Freund-Rubin compactification from thermodynamic and dynamical perspectives. Freund-Rubin compactification allows not only trivial solutions but also warped solutions describing warped product of external de Sitter space and internal deformed sphere. We study dynamical stability by analyzing linear perturbations around solutions in each branch. Also we study thermodynamic stability based on de Sitter entropy. We show complete agreement of thermodynamic and dynamical stabilities of this system. Finally, we interpret the results in terms of effective energy density in the four-dimensional Einstein frame and discuss cosmological implications.