Generalized Kaluza-Klein Theory Research Articles

Measuring the dimensionality of compact extra dimensions with inspiral gravitational waves from black-hole binaries

Gravitational waves from coalescing black-hole binaries (BHBs) were recently observed by the advanced LIGO detectors. Based on the perturbation analysis, for general Kaluza-Klein theories with compact extra dimensions, we find a 1st-order post-Newtonian correction to the inspiral gravitational waveforms of black-hole binaries, that comes from the variations of the volume of the extra dimensions in near source zones. Such correction depends on a new parameter with n the dimensionality of the extra space and it is irrelevant to the particular choice of the topology of the extra space. For the ideal case of a black-hole binary system following nearly circular orbital motion with almost equal or intermediate mass ratio, such higher-dimensional corrections to the chirping amplitude are worked out. Giving the power of tracing inspiral waves from coalescing massive BHBs with high signal-to-noise ratios, the planned space-borne antennas such as the eLISA and DECIGO may give us a measurement of the parameter χ in the near future and may serve us as new probes in the searching for the evidence of the hidden compact dimensions.

On the extra force in brane world scenario

In the study of the dynamics in a 5D bulk from brane world scenario, an extra force with abnormal properties was detected (cf. [D. Youm, Extra force in brane worlds, Phys. Rev. D62 (2000) 084002; D. Youm, Null geodesics in brane world universe, Mod. Phys. Lett. A16 (2001) 2371; L. F. Zhang and Y. Z. Zhang, Null geodesics in brane world scenarios, Commun. Theor. Phys. (Beijing)41 (2004) 48]). In this paper, by using the Riemannian horizontal connection introduced in [A. Bejancu, A new point of view on general Kaluza–Klein theories, Progr. Theor. Phys.128 (2012) 541], we give a new definition for the extra force in a 5D bulk, and show that it does not contradict the 4D physics. In particular, we show that this force appears very rarely along geodesics in a warped 5D bulk.

A New Point of View on General Kaluza-Klein Theories

A New Point of View on General Kaluza-Klein Theories

Preheating with extra dimensions

We investigate preheating in a higher-dimensional generalized Kaluza-Klein theory with a quadratic inflaton potential $V(\phi)=\frac12 m^2\phi^2$ including metric perturbations explicitly. The system we consider is the multi-field model where there exists a dilaton field $\sigma$ which corresponds to the scale of compactifications and another scalar field $\chi$ coupled to inflaton with the interaction $\frac12 g^2\phi^2\chi^2+\tilde{g}^2\phi^3\chi$. In the case of $\tilde{g}=0$, we find that the perturbation of dilaton does not undergo parametric amplification while the $\chi$ field fluctuation can be enhanced in the usual manner by parametric resonance. In the presence of the $\tilde{g}^2\phi^3\chi$ coupling, the dilaton fluctuation in sub-Hubble scales is modestly amplified by the growth of metric perturbations for the large coupling $\tilde{g}$. In super-Hubble scales, the enhancement of the dilaton fluctuation as well as metric perturbations is weak, taking into account the backreaction effect of created $\chi$ particles. We argue that not only is it possible to predict the ordinary inflationary spectrum in large scales but extra dimensions can be held static during preheating in our scenario.

Are Kaluza-Klein modes enhanced by parametric resonance?

We study parametric amplification of Kaluza-Klein (KK) modes in a higher $D\ensuremath{-}\mathrm{dimensional}$ generalized Kaluza-Klein theory, which was originally considered by Mukohyama in the narrow resonance case. It was suggested that KK modes can be enhanced by an oscillation of a scale of compactification by the $d\ensuremath{-}\mathrm{dimensional}$ sphere ${S}^{d} (d=D\ensuremath{-}4)$ and by the direct product ${S}^{{d}_{1}}\ifmmode\times\else\texttimes\fi{}{S}^{{d}_{2}} {(d}_{1}{+d}_{2}=D\ensuremath{-}4).$ We extend this past work to the more general case where initial values of the scale of compactification and the quantum number of the angular momentum $l$ of KK modes are not small. We perform analytic approaches based on the Mathieu equation as well as numerical calculations, and find that the expansion of the universe rapidly makes the KK field deviate from instability bands. As a result, KK modes are not enhanced sufficiently in an expanding universe in these two classes of models.

Cosmological solution in multidimensional gravitation based on principal layering

Multidimensional gravitation based on principal layering, the basis of which is four-dimensional Einsteinian space-time while the layers are the SU(2) gage group, is considered. In the spirit of ideas in generalized Kaluza-Klein theories, gage fields correspond to the nondiagonal components of the multidimensional metric in this theory. A cosmological solution is obtained on the basis of an instant-like ansatz for nondiagonal components of the multidimensional metric. It is shown that, at least locally, this solution has a bounce; its behavior near the singularity is investigated.

Excitation of a Kaluza-Klein mode by parametric resonance

In this paper we investigate a parametric resonance phenomenon of a Kaluza-Klein mode in a $D$-dimensional generalized Kaluza-Klein theory. As the origin of the parametric resonance we consider a small oscillation of a scale of the compactification around a present-day value of it. To make our arguments definite and for simplicity we consider two classes of models of the compactification: those by ${S}_{d}$ $(d=D\ensuremath{-}4)$ and those by ${S}_{{d}_{1}}\ifmmode\times\else\texttimes\fi{}{S}_{{d}_{2}}$ ${(d}_{1}>~{d}_{2},$ ${d}_{1}{+d}_{2}=D\ensuremath{-}4).$ For these models we show that parametric resonance can occur for the Kaluza-Klein mode. After that, we give formulas of a creation rate and a number of created quanta of the Kaluza-Klein mode due to the parametric resonance, taking into account the first and the second resonance bands. By using the formulas we calculate those quantities for each model of compactification. Finally we give conditions for the parametric resonance to be efficient and discuss cosmological implications.

The role of the internal metric in generalized Kaluza–Klein theories

The dimensional reduction of a Weyl space WN of N=4+n dimensions to a principal fiber bundle P̃(W4,G̃n) over a four-dimensional space–time W4 with structural group G̃n of dimension n arising from the existence of n conformal Killing vector fields of the original N-metric is studied. The framework of a Weyl geometry is adopted in order to investigate conformal rescalings of the metric on the bundle P̃(W4,G̃n) obtained. The Weyl symmetry is then, finally, broken again by choosing a particular Weyl gauge in which the internal, i.e., fiber metric, is of constant Cartan–Killing form. This choice of gauge, yielding a Riemannian theory, forces the internal metric to play no dynamical role in the theory, as is usually assumed to be the case in non-Abelian gauge theories. However, this gauge induces a conformal transformation of the metric in the space–time base of P̃ compared to the space–time metric obtained by the ordinary Kaluza–Klein reduction of a Riemannian space VN. The role of vector torsion in this dimensional reduction by isometries and scale transformations is also investigated.

Fermion masses and cosmology in multidimensional unified theories

A possible method of obtaining massless fermions and a zero cosmological constant within the context of generalized Kaluza-Klein theories by introducing random constant fields having support over all space is presented. It is seen that this can be achieved through the presence of a random magnetic condensate and that such a result can be related to the presence of vorticity in the additional (hidden) dimensions.

Non-abelian Kaluza-Klein monopoles

I classify magnetic monopoles in general Kaluza-Klein theories. The construction of monopole solutions is explicitly carried out for an SO(3) model.

Induced Einstein-Hilbert-Yang-Mills action from quantum effects in generalized Kaluza-Klein theory

It is shown how the Einstein-Hilbert-Yang-Mills action may be induced from quantized matter fields on a non-abelian Kaluza-Klein background. General formulae are derived in the case of a quantized scalar field when the extra dimensions form a coset space. Explicit results are obtained in the special case of odd-dimensional spheres.

Poincaré gauge theory, gravitation, and transformation of matter fields

AbstractIn the generalized Kaluza‐Klein theories a (4 + N)‐dimensional Riemannian space is used as a configuration space to unify gravitation with a nonabelien gauge symmetry characterized by a gauge group G of order N. The original metric space V4+N, however, is broken down in these theories to a local product structure M4 × VN (M4 being Minkowski space‐time) leading thereby to a description in terms of a fiber bundle over space‐time V4 with structural group G. In this paper we base the discussion from the very beginning on a bundle structure as the underlying geometric stratum and treat the quantum mechanical aspect of matter by representing it in the form of a generalized wave function, ϕ(x, X), defined as a section on a fiber bundle associated to a principal G‐bundle over space time having a homogeneous space of the group G as fiber. To make contact with gravitation we consider various soldered bundles possessing the Poincaré group, G = ISO(3, 1), as structural or gauge group and define Poincaré gauge fields as generalized matter fields on them. After reviewing the formulation of general relativity as a gauge theory of the Lorentz group we turn to the affine case and present a geometric formulation of a Poincaré gauge theory based on a Riemann‐Cartan space‐time U4 with axial vector torsion. Two sets of field equations are discussed relating the material source quantities to the geometric fields. Besides Einstein's equations coupling the metric to the classical distribution of energy and momentum of matter a second set of nonlinear field equations is set up relating a bilinear current in the Poincaré gauge fields to the axial vector torsion field of the underlying space‐time geometry. Finally, a breaking of the Poincaré symmetry is introduced in a manner involving the generalized matter field ϕ(x, X) freezing thereby the translational gauge degrees of freedom, however, leaving the Lorentz gauge symmetry unaffected.

Quantum effects in generalized Kaluza-Klein theories

Quantum effects are studied in Kaluza-Klein theories with a torus Tn as the extra space. It is shown that some of the physical circumferences of Tn tend to contract to sizes of the order of the Planck length due to quantum effects. This behaviour of contraction or expansion of the compact dimensions depends on their initial values.

Gauge Symmetries in Generalized Kaluza-Klein Theories

Gauge Symmetries in Generalized Kaluza-Klein Theories

On Riemannian spaces with conformal symmetries or a tool for the study of generalized Kaluza–Klein theories

The Riemann geometry of a space with conformal symmetries is written in terms of intrinsic objects defined from the action of the symmetries. Its application in the study of generalized Kaluza–Klein theories is discussed.

Grand unification near the Kaluza-Klein scale

The supersymmetric grand unification scale is close to the calculable size ≈10 −17 GeV −1 of the extra space dimensions of generalized Kaluza-Klein theory. Grand unification may therefore be a high-dimensional phenomenon with consequences also for cosmology.

Kaluza-Klein cosmologies

In generalized Kaluza-Klein theories the scale set by the size of the extra space-dimensions is close to the grand unification scale of supersymmetric GUT's with minimal number of Higgs supermultiplets. In view of this observation, we explore cosmologies in which the “effective” dimensionality of space depends on time. Such cosmologies are studied in higher-dimensional Jordan-Brans-Dicke theories, and in 10- and 11-dimensional supergravity. The preferential expansion of three space-like dimensions is noted in the latter theory. Cosmology in pure higher-dimensional Einstein theory, where there is no preferential expansion of three space-like dimensions, has been discussed by Chodos and Detweiler.