SPACE, TIME AND FUNDAMENTAL INTERACTIONS

LONGITUDINAL WAVES IN 5D ABSOLUTE PARALLELISM AND RELATIVISTICALLY EXPANDING BRANE COSMOLOGY

Zhogin I.L.

The standard \(4D\)-cosmology within general relativity is by no means an «island» solution satisfying trivial boundary conditions; with negative or zero spatial curvature, the number of galaxies is infinite, which is rather unphysical. A five-dimensional cosmology is proposed, the Universe-on-a-brane, arising in an exceptional variant of Absolute Parallelism (AP). This exceptional equation (EE), of the second order, of the frame field \(h^a_{\mu}\), does not admit, apparently, singularities of solutions if \(D = 5\). The EE’s compatibility, regularity of its highest derivatives, breaks (unlike other cases, including the GR vacuum equation), when \(h^a_{\mu}\) (and the co-metric) becomes one-degenerate. EE has no exact conservation laws, but there is a covariantly conserved stress-energy tensor, as well as \(O4\)-symmetric solutions looking as a longitudinal wave going along the radius, in which, as in a shallow optical waveguide (or a thick brane), shorter almost tangential waves can be held, as well as quasi-particles – nonlinear field configurations, carrying a topological charge and/or quasi-charge (‘or’ for bosons). Brane thickness (in the co-moving system; \(L\sim 3-5\) kau) sets the distance where attraction \(\sim 1/r^2\) is replaced by the slower law \(1/r\).

The brane velocity \(\) is slightly less than \(1\) (\(c = 1\)) because the brane holds energy-carrying waves – three of the 15 polarizations; others, including three growing, linearly unstable polarizations responsible for nonlinearities and quasi-particles, do not carry energy. Motion of massive bodies and massless photons in such a relativistically expanding brane is briefly considered, as well as possible manifestations of non-linear off-brane «actors».

A tabletop experiment (an oscillating pendulum, spherical capacitor, ...) and an electro-gravitational effect are briefly discussed which are able to confirm the existence of longitudinal waves directly changing the metric and Ricci tensor.