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Kerner R.
Introduction to the Unimodular Kaluza — Klein theory / Kerner R., Fabris J. C. - Текст на англ. языке // Физические интерпретации теории относительности, Международная научная конференция 24-я, Москва, 7 - 10 июля 2025 г. = Physical Interpretations of Relativity Theory (PIRT–2025) : сборник тезисов / МГТУ им. Н. Э. Баумана. - М., 2025. -
Unimodular Gravity was first introduced by Einstein as early as in 1919. The extra unimodularity condition imposed on the pseudo-Riemannian metric seemed to be a promising alternative to the cosmological constant, by using the condition det(g) = 1 as a Lagrange multiplier in the Einstein — Hilbert variational principle. In this talk, we shall investigate physical and mathematical aspects of extension of the unimodularity condition to the 5-dimensional Kaluza — Klein space. It turns out that when the unimodularity constraint applies to the five dimensional equations, it does not necessarily apply to the reduced equations in four dimensions. The reduction of the five dimensional equations to four dimensions leads to a quite unusual structure connecting gravity to a scalar field and ordinary matter, which stems from the five dimensional framework. Cosmological vacuum solutions of the effective four dimensional equations have been derived in our recent paper [1]. They describe a symmetrically bouncing universe. However, even if the four dimensional metric is free of singularities, the original five dimensional one becomes degenerate at the bounce since the modulus field associated with the fifth dimension vanishes at the transition point from the contracting to the expanding phase.
