On the Stability of Non-Singular Solutions in Effective Theory from Kaluza-Klein Unimodular Gravity

TL;DR

This paper explores a novel scalar-tensor theory derived from five-dimensional unimodular Kaluza-Klein gravity, revealing non-singular cosmological solutions but also instabilities in gravitational wave propagation.

Contribution

It introduces a new class of scalar-tensor theories from unimodular Kaluza-Klein reduction and analyzes their stability and physical implications.

Findings

Vacuum solutions exhibit bouncing, non-singular behavior

Gravitational waves show instabilities related to higher-dimensional structure

Comparison with quantum models highlights similar background features

Abstract

Unimodular theory incorporating the Kaluza-Klein construction in five dimensions leads, after reduction to four dimensions, to a new class of scalar-tensor theory. The vacuum cosmological solutions display a bouncing, non singular behavior. From the four dimensional point of view, the solutions are completely regular. However, the propagation of gravitational waves in this geometry displays the presence of instabilities which reflect some features of the original five dimensional structure. Comparison with a four dimensional quantum model with cosmological constant, which has a similar background behavior, is discussed.