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Kaluza-Klein theories of a five-dimensional spacetime yield not only the equations of general relativity and electromagnetism, but also a scalar field. This scalar field, sometimes quantised as the radion or dilaton, is thought not to exist.

Given today's twin puzzles of Universal expansion, dubbed dark energy, and gravitational anomalies on the galactic scale, dubbed dark matter, (how) can we be sure that the Kaluza-Klein scalar is not involved in either of them?

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3 Answers 3

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Yes, Kaluza-Klein excitations might be the dark matter. See e.g. this search on arxiv.org for some papers making the connection. In particular the earliest references there (on the second page) might be most useful for you.

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  • $\begingroup$ Thank you. I see that a similar search on KK with dark energy also yields a few papers. $\endgroup$ Commented Nov 10, 2020 at 19:40
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Just wanted to add to the other answer, that the current outlook for a Kaluza-Klein-type theory being the answer for dark matter, and dark energy also, isn't compelling. There are of course people who've considered such models because they're phenomenologically interesting, but they're either under stringent constraints or have theoretical issues, especially for dark energy in both late-time cosmology and inflationary cosmology (see Section 5 of Modified Gravity and Cosmology for a quick discussion on the current outlook).

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Question is about how Kaluza might enlighten us on universal expansion and dark matter. The matter model which I think is correct is the rotating wave of electron (or fermions). It has 5 vectors of which 3 are space of course. The other two are rotation and expansion. Let us consider a position vector: Pc = EvPv + EtPt. EvPv is to represent 3D space and we will keep it in constant direction to keep things simple. At the end of the EvPv let us attach the rotor (rotating vector) EtPt that is always perpendicular to EvPv. Differentiating with respect to time we get: dPc/dt = EvVv + ErVr + EtVt. We need the EtVt so we can get curvature in the Rkl calculation of the 4-space. If Vt = 0, then we would just have the cylinder condition and no intrinsic curvature. That Vt allows the Rotating Wave to spiral in or out and thus leads to space expansion.

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