Classical and quantized aspects of dynamics in five dimensional relativity

A null path in 5D can appear as a timelike path in 4D, and for a certain gauge in 5D the motion of a massive particle in 4D obeys the usual quantization rule with an uncertainty-type relation. Generalizations of this result are discussed in regard to induced-matter and membrane theory.Comment: 26 pages, in press in Class. Quant. Gra

FLRW Universes from "Wave-Like" Cosmologies in 5D

We consider the evolution of a 4D-universe embedded in a five-dimensional (bulk) world with a large extra dimension and a cosmological constant. The cosmology in 5D possesses "wave-like" character in the sense that the metric coefficients in the bulk are functions of the extra coordinate and time in a way similar to a pulse or traveling wave propagating along the fifth dimension. This assumption is motivated by some recent work presenting the big-bang as a higher dimensional shock wave. We show that this assumption, together with an equation of state for the effective matter quantities in 4D, allows Einstein's equations to be fully integrated. We then recover the familiar FLRW universes, on the four-dimensional hypersurfaces orthogonal to the extra dimension. Regarding the extra dimension we find that it is {\em growing} in size if the universe is speeding up its expansion. We also get an estimate for the relative change of the extra dimension over time. This estimate could have important observational implications, notably for the time variation of rest mass, electric charge and the gravitational "constant". Our results extend previous ones in the literature.Comment: Few comments added, references updated. To appear in Int. J. of Mod. Phys.

Quantum cosmology of 5D non-compactified Kaluza-Klein theory

We study the quantum cosmology of a five dimensional non-compactified Kaluza-Klein theory where the 4D metric depends on the fifth coordinate, $x^4\equiv l$. This model is effectively equivalent to a 4D non-minimally coupled dilaton field in addition to matter generated on hypersurfaces l=constant by the extra coordinate dependence in the four-dimensional metric. We show that the Vilenkin wave function of the universe is more convenient for this model as it predicts a new-born 4D universe on the $l\simeq0$ constant hypersurface.Comment: 14 pages, LaTe

The bang of a white hole in the early universe from a 6D vacuum state: Origin of astrophysical spectrum

Using a previously introduced model in which the expansion of the universe is driven by a single scalar field subject to gravitational attraction induced by a white hole during the expansion (from a 6D vacuum state), we study the origin of squared inflaton fluctuations spectrum on astrophysical scales.Comment: Final version to be published in Eur. Phys. J.

Null Geodesics in Five Dimensional Manifolds

We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricci-flat, then there is an induced cosmological constant in the 4D sub-manifold. We derive the general form of the 5D Killing vectors and relate them to the 4D Killing vectors of the embedded spacetime. We then study the 5D null geodesic paths and show that the 4D part of the motion can be timelike -- that is, massless particles in 5D can be massive in 4D. We find that if the null trajectories are affinely parameterized in 5D, then the particle is subject to an anomalous acceleration or fifth force. However, this force may be removed by reparameterization, which brings the correct definition of the proper time into question. Physical properties of the geodesics -- such as rest mass variations induced by a variable cosmological ``constant'', constants of the motion and 5D time-dilation effects -- are discussed and are shown to be open to experimental or observational investigation.Comment: 19 pages, REVTeX, in press in Gen. Rel. Gra

An exact solution of the five-dimensional Einstein equations with four-dimensional de Sitter-like expansion

We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.Comment: 6 pages; to appear in Journal of Mathematical Physics; v2: reference 3 correcte

Extra symmetry in the field equations in 5D with spatial spherical symmetry

We point out that the field equations in 5D, with spatial spherical symmetry, possess an extra symmetry that leaves them invariant. This symmetry corresponds to certain simultaneous interchange of coordinates and metric coefficients. As a consequence a single solution in 5D can generate very different scenarios in 4D, ranging from static configurations to cosmological situations. A new perspective emanates from our work. Namely, that different astrophysical and cosmological scenarios in 4D might correspond to the same physics in 5D. We present explicit examples that illustrate this point of view.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit

Stochastic emergence of inflaton fluctuations in a SdS primordial universe with large-scale repulsive gravity from a 5D vacuum

We develop a stochastic approach to study scalar field fluctuations of the inflaton field in an early inflationary universe with a black-hole (BH), which is described by an effective 4D SdS metric. Considering a 5D Ricci-flat SdS static metric, we implement a planar coordinate transformation, in order to obtain a 5D cosmological metric, from which the effective 4D SdS metric can be induced on a 4D hypersurface. We found that at the end of inflation, the squared fluctuations of the inflaton field are not exactly scale independent and becomes sensitive with the mass of the BH.Comment: version accepted in European Physical Journal Plu

Induced Matter and Particle Motion in Non-Compact Kaluza-Klein Gravity

We examine generalizations of the five-dimensional canonical metric by including a dependence of the extra coordinate in the four-dimensional metric. We discuss a more appropriate way to interpret the four-dimensional energy-momentum tensor induced from the five-dimensional space-time and show it can lead to quite different physical situations depending on the interpretation chosen. Furthermore, we show that the assumption of five-dimensional null trajectories in Kaluza-Klein gravity can correspond to either four-dimensional massive or null trajectories when the path parameterization is chosen properly. Retaining the extra-coordinate dependence in the metric, we show the possibility of a cosmological variation in the rest masses of particles and a consequent departure from four-dimensional geodesic motion by a geometric force. In the examples given, we show that at late times it is possible for particles traveling along 5D null geodesics to be in a frame consistent with the induced matter scenario.Comment: 29 pages, accepted to GR