Abstract
Unimodular gravity became an object of increasing interest in the late 80-ties (see, e.g. M. Henneaux and C. Teitelboim, (1989 Phys. Lett. B 222, 195), W. Buchmüller and N. Dragon, N. (1989 Phys. Lett. B 223, 313), W.G. Unruh, (1989 Phys. Rev. D, 40, 1048) and was recently used in primordial Universe modeling with cosmological constant, in the context of the Brans-Dicke gravity including scalar field A. M. Almeida et al (2023 Universe 8, 429). In the present article we investigate the possibility of imposing the unimodular condition within the 5-dimensional Kaluza-Klein theory including the scalar field. The 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 is then presented and discussed.
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