One particular variant of Kaluza–Klein theory is space-time-matter theory or induced matter theory, chiefly promulgated by Paul Wesson and other members of the so-called Space-Time-Matter Consortium. In this version of the theory, it is noted that solutions to the equation
with RAB the five-dimensional Ricci curvature, may be re-expressed so that in four dimensions, these solutions satisfy Einstein's equations
with the precise form of the Tμν following from the Ricci-flat condition on the five-dimensional space. Since the energy-momentum tensor Tμν is normally understood to be due to concentrations of matter in four-dimensional space, the above result is interpreted as saying that four-dimensional matter is induced from geometry in five-dimensional space.
In particular, the soliton solutions of RAB = 0 can be shown to contain the Friedmann-Lemaitre-Robertson-Walker metric in both radiation-dominated (early universe) and matter-dominated (later universe) forms. The general equations can be shown to be sufficiently consistent with classical tests of general relativity to be acceptable on physical principles, while still leaving considerable freedom to also provide interesting cosmological models.
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