Wave Mechanics and General Relativity: A Rapprochement

Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality

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.

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

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

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

An Embedding for General Relativity and its Implications for New Physics

We show that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of the 5D Ricci-flat equations with an effective 4D cosmological "constant" that is a specific function of the extra coordinate. For unified theories of the forces in higher dimensions, this has major physical implications

The Behavior of Kasner Cosmologies with Induced Matter

We extend the induced matter model, previously applied to a variety of isotropic cases, to a generalization of Bianchi type-I anisotropic cosmologies. The induced matter model is a 5D Kaluza-Klein approach in which assumptions of compactness are relaxed for the fifth coordinate, leading to extra geometric terms. One interpretation of these extra terms is to identify them as an ``induced matter'' contribution to the stress-energy tensor. In similar spirit, we construct a five dimensional metric in which the spatial slices possess Bianchi type-I geometry. We find a set of solutions for the five dimensional Einstein equations, and determine the pressure and density of induced matter. We comment on the long-term dynamics of the model, showing that the assumption of positive density leads to the contraction over time of the fifth scale factor.Comment: 14 page

Gravitational conformal invariance and coupling constants in Kaluza-Klein theory

We introduce a generalized gravitational conformal invariance in the context of non-compactified 5D Kaluza-Klein theory. It is done by assuming the 4D metric to be dependent on the extra non-compactified dimension. It is then shown that the conformal invariance in 5D is broken by taking an absolute cosmological scale $R_0$ over which the 4D metric is assumed to be dependent weakly on the 5th dimension. This is equivalent to Deser's model for the breakdown of the conformal invariance in 4D by taking a constant cosmological mass term $\mu^2\sim R_0^{-2}$ in the theory. We set the scalar field to its background cosmological value leading to Einstein equation with the gravitational constant $G_N$ and a small cosmological constant. A dual Einstein equation is also introduced in which the matter is coupled to the higher dimensional geometry by the coupling $G_N^{-1}$. Relevant interpretations of the results are also discussed.Comment: 10 pages, LaTeX, some cghanges in the tex

Modern cosmologies from empty Kaluza-Klein solutions in 5D

We show that the empty five-dimensional solutions of Davidson-Sonnenschtein-Vozmediano, {\em Phys. Rev.} {\bf D32} (1985)1330, in the "old" Kaluza-Klein gravity, under appropriate interpretation can generate an ample variety of cosmological models in 4D, which include the higher-dimensional modifications to general relativity predicted by "modern" versions of noncompactified 5D gravity as, e.g., induced-matter and braneworld theories. This is the first time that these solutions are investigated in a systematic way as embeddings for cosmological models in 4D. They provide a different formulation, which is complementary to the approaches used in current versions of 5D relativity.Comment: Accepted for publication in JHE

Inducing the cosmological constant from five-dimensional Weyl space

We investigate the possibility of inducing the cosmological constant from extra dimensions by embedding our four-dimensional Riemannian space-time into a five-dimensional Weyl integrable space. Following approach of the induced matter theory we show that when we go down from five to four dimensions, the Weyl field may contribute both to the induced energy-tensor as well as to the cosmological constant, or more generally, it may generate a time-dependent cosmological parameter. As an application, we construct a simple cosmological model which has some interesting properties.Comment: 7 page