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

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 bounce with non-singular behavior the effective lower dimension model: 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 singular features of the original five-dimensional structure connected to a degenerate metric at the bounce. A four-dimensional quantum model with cosmological constant, which has a similar background behavior, is discussed and revealed to be stable.