Perturbative analysis of singularity-free cosmological solutions in unimodular Kaluza-Klein theory

TL;DR

This paper analyzes the stability of singularity-free cosmological solutions in unimodular Kaluza-Klein theory through perturbative methods, revealing insights into their robustness against small fluctuations.

Contribution

It provides a perturbative stability analysis of singularity-free cosmological solutions within unimodular Kaluza-Klein theory, extending previous solutions with new insights.

Findings

Solutions are stable against small perturbations

Scalar field influences stability properties

Perturbative analysis suggests robustness of solutions

Abstract

The unimodular version of the Kaluza-Klein theory is briefly recalled, and its projection on the $4$-dimensional spacetime is constructed. Imposing unimodularity condition on the $5$-dimensional Kaluza-Klein metric, det$g_{AB}=1$ is equivalent with introducing cosmological term in Einstein's equations in $4$ dimensions, and with scalar field of the Brans-Dicke type. Singularity-free cosmological solutions with scalar field and with matter sources are constructed, and their basic properties analyzed, along the results obtained in previous publications. In the present paper, attention is focussed on the perturbative analysis of cosmological solutions, providing a clue concerning their stability against small fluctuations.