A Five-dimensional Kaluza-Klein Approach to Unimodular Gravity

In this article we present a possibility of imposing the unimodular condition within the 5-dimensional Kaluza-Klein theory including the scalar field. Unimodular gravity became an object of increasing interest in the late 80-ties; and was recently used in primordial Universe modeling with cosmological constant, in the context of the Brans-Dicke gravity including scalar field. A generalization of the unimodularity principle to the 5-dimensional Kaluza-Klein model was discussed in our recent paper, in which variational principle is formulated in 5 dimensions first, and dimensional reduction is applied to the resulting set of equations. A cosmological model based on these equations was then presented and discussed. Here we present further developments of this approach, focussing our attention at perturbative aspects and stability of solutions.