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

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

Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes

Equations for submanifolds, which correspond to embeddings of the four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are presented in convenient form in general case. Several specific examples are considered.Comment: 7 pages, LaTeX, the mathematical part of this paper is based on the withdrawn preprint arXiv:1012.0320 [gr-qc

Wesson's IMT with a Weylian bulk

The foundations of Wesson's induced matter theory are analyzed. It is shown that the 5D empty bulk must be regarded rather as a Weylian space than as a Riemannian one.The framework of a Weyl-Dirac version of Wesson's theory is elaborated and discussed. The bulk possesses in addition to the metric tensor a Weylian connection vector as well Dirac's gauge function; there are no sources (mass, current) in the bulk. On the 4D brane one obtains a geometrically based unified theory of gravitation and electromagnetism with mass, currents and equations induced by the 5D bulkComment: 29 page

The Big Bang as a Phase Transition

We study a five-dimensional cosmological model, which suggests that the universe bagan as a discontinuity in a (Higgs-type) scalar field, or alternatively as a conventional four-dimensional phase transition.Comment: 10 pages, 2 figures; typo corrected in equation (18); 1 reference added; version to appear in International Journal of Modern Physics

On the embedding of branes in five-dimensional spaces

We investigate the embedding of four-dimensional branes in five-dimensional spaces. We firstly consider the case when the embedding space is a vacuum bulk whose energy-momentum tensor consists of a Dirac delta function with support in the brane. We then consider the embedding in the context of Randall-Sundrum-type models, taking into account $Z_{2}$ symmetry and a cosmological constant. We employ the Campbell-Magaard theorem to construct the embeddings and are led to the conclusion that the content of energy-matter of the brane does not necessarily determine its curvature. Finally, as an application to illustrate our results, we construct the embedding of Minkowski spacetime filled with dust.Comment: 12 pages - REVTEX To appear in Classical and Quantum Gravit

Phantom cosmology with a decaying cosmological function Λ(t)\Lambda(t) induced from five-dimensional (5D) geometrical vacuum

Introducing a variable cosmological function $\Lambda (t)$ in a geometrical manner from a 5D Riemann-flat metric, we investigate the possibility of having a geometrical criterion to choose a suitable cosmological function $\Lambda (t)$ for every 4D dynamical hypersurface capable of generate phantom cosmologies.Comment: final versio

Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim

In classical Kaluza-Klein theory, with compactified extra dimensions and without scalar field, the rest mass as well as the electric charge of test particles are constants of motion. We show that in the case of a large extra dimension this is no longer so. We propose the Hamilton-Jacobi formalism, instead of the geodesic equation, for the study of test particles moving in a five-dimensional background metric. This formalism has a number of advantages: (i) it provides a clear and invariant definition of rest mass, without the ambiguities associated with the choice of the parameters used along the motion in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the discussion, and (iii) we avoid the difficulties associated with the "splitting" of the geodesic equation. For particles moving in a general 5D metric, we show how the effective rest mass, as measured by an observer in 4D, varies as a consequence of the large extra dimension. Also, the fifth component of the momentum changes along the motion. This component can be identified with the electric charge of test particles. With this interpretation, both the rest mass and the charge vary along the trajectory. The constant of motion is now a combination of these quantities. We study the cosmological variations of charge and rest mass in a five-dimensional bulk metric which is used to embed the standard k = 0 FRW universes. The time variations in the fine structure "constant" and the Thomson cross section are also discussed.Comment: V2: References added, discussion extended. V3 is identical to V2, references updated. To appear in General Relativity and Gravitatio

Equivalence Between Space-Time-Matter and Brane-World Theories

We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and non-local high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we notice that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let