Induced Matter Theory Research Articles

Noncompactified Kaluza–Klein Gravity

We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space–Time–Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans–Dicke theory and the modified Sáez–Ballester theory are briefly explained. Finally, we apply the latter to the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological models in arbitrary dimensions and analyze the corresponding solutions.

Accounting for exotic matter and the extreme radial tension in Morris\u2013Thorne wormholes of embedding class one

The embedding of a curved spacetime in a higher-dimensional flat spacetime has continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. Einstein’s theory allows the fifth dimension to be either spacelike or timelike. By assuming the latter, this paper addresses two fundamental issues concerning Morris–Thorne wormholes, the origin of exotic matter and the frequently inexplicable enormous radial tension at the throat.

Late time cosmic acceleration in modified Sáez–Ballester theory

We establish an extended version of the modified S\'{a}ez-Ballester (SB) scalar-tensor theory in arbitrary dimensions whose energy momentum tensor as well as potential are pure geometrical quantities. This scenario emerges by means of two scalar fields (one is present in the SB theory and the other is associated with the extra dimension) which widens the scope of the induced-matter theory. Moreover, it bears a close resemblance to the standard S\'{a}ez-Ballester scalar-tensor theory, as well as other alternative theories to general relativity, whose construction includes either a minimally or a non-minimally coupled scalar field. However, contrary to those theories, in our framework the energy momentum tensor and the scalar potential are not added by hand, but instead are dictated from the geometry. Concerning cosmological applications, our herein contribution brings a new perspective. We firstly show that the dark energy sector can be naturally retrieved within a strictly geometric perspective, and we subsequently analyze it. Moreover, our framework may provide a hint to understand the physics of lower gravity theories.

Extended anisotropic models in noncompact Kaluza–Klein theory

In this paper, new exact solutions for locally rotational symmetric (LRS) space-times are obtained within the modified Brans–Dicke theory (MBDT) (Rasouli et al 2014 Class. Quantum Grav. 31 115002). Specifically, extended five-dimensional (5D) versions of Kantowski–Sachs, LRS Bianchi type I and Bianchi type III are investigated in the context of the standard Brans–Dicke theory. We subsequently extract their corresponding dynamics on a 4D hypersurface. Our results are discussed regarding others obtained in the standard Brans–Dicke theory, induced-matter theory and general relativity. Moreover, we comment on the evolution of the scale factor of the extra spatial dimension, which is of interest in Kaluza–Klein frameworks.

Interacting Induced Dark Energy Model

Following the idea of the induced matter theory, for a non-vacuum five-dimensional version of general relativity, we propose a model in which the induced terms emerging from the extra dimension in our four-dimensional space-time, supposed to be as dark energy. Then we investigate the FLRW type cosmological equations and illustrate that when the scale factor of the fifth dimension has no dynamics, in early time the universe expands with deceleration and then in late time, expands with acceleration. In this case, the state parameter of the effective dark energy has a range of $-1<\bar{w}_{_{X}}<0$ and it has the value $-1/2$ for present time. The results for current acceleration impose that $\Omega_{_{X\circ}}>2\Omega_{_{M\circ}}$ which is in agreement with the measurements. We show that the effective energy density of dark energy have been having the same order of magnitude of the effective energy density of matter from the early time in the decelerating epoch of the universe expansion until now. The model avoids the cosmological coincidence problem.

Modified Saez–Ballester scalar–tensor theory from 5D space-time

In this paper, we bring together the five-dimensional Saez–Ballester (SB) scalar–tensor theory (Saez and Ballester 1986 Phys. Lett. 113A 9) and the induced-matter-theory (IMT) setting (Wesson and Ponce de Leon 1992 J. Math. Phys. 33 3883), to obtain a modified SB theory (MSBT) in four dimensions. Specifically, by using an intrinsic dimensional reduction procedure into the SB field equations in five-dimensions, a MSBT is obtained onto a hypersurface orthogonal to the extra dimension. This four-dimensional MSBT is shown to bear distinctive new features in contrast to the usual corresponding SB theory as well as to IMT and the modified Brans–Dicke theory (MBDT) (Rasouli et al 2014 Class. Quantum Grav. 31 115002). In more detail, besides the usual induced matter terms retrieved through the IMT, the MSBT scalar field is provided with additional physically distinct (namely, SB induced) terms as well as an intrinsic self-interacting potential (interpreted as a consequence of the IMT process and the concrete geometry associated with the extra dimension). Moreover, our MSBT has four sets of field equations, with two sets having no analog in the standard SB scalar–tensor theory. It should be emphasized that the herein appealing solutions can emerge solely from the geometrical reductional process, from the presence also of extra dimension(s) and not from any ad-hoc matter either in the bulk or on the hypersurface. Subsequently, we apply the herein MSBT to cosmology and consider an extended spatially flat FLRW geometry in a five-dimensional vacuum space-time. After obtaining the exact solutions in the bulk, we proceed to construct, by means of the MSBT setting, the corresponding dynamic, on the four-dimensional hypersurface. More precisely, we obtain the (SB) components of the induced matter, including the induced scalar potential terms. We retrieve two different classes of solutions. Concerning the first class, we show that the MSBT yields a barotropic equation of state for the induced perfect fluid. We then investigate vacuum, dust, radiation, stiff fluid and false vacuum cosmologies for this scenario and contrast the results with those obtained in the standard SB theory, IMT and BD theory. Regarding the second class solutions, we show that the scale factor behaves in a similar way to a de Sitter (DeS) model. However, in our MSBT setting, this behavior is assisted by non-vanishing induced matter instead, without any a priori cosmological constant. Moreover, for all these solutions, we show that the extra dimension contracts with the cosmic time.

Λ(t)CDM and the present accelerating expansion of the universe from 5D scalar vacuum

Abstract In this letter we investigate some consequences of considering our 4D observable universe as locally and isometrically embedded in a 5D spacetime, where gravity is described by a Brans–Dicke theory in vacuum. Once we impose the embedding conditions we obtain that gravity on the 4D spacetime is governed by the Einstein field equations modified by an extra term that can play the role of a dynamical cosmological constant. Two examples were studied. In the first we derive a cosmological model of a universe filled only with a cosmological constant. In the second we obtain a cosmological solution describing a universe filled with matter, radiation and a dynamical cosmological constant. We constrain the model by using the current observational data combination Planck + WP + BAO + SN. The present acceleration in the expansion of the universe is explained by the geometrically induced dynamical cosmological constant avoiding the introduction of a dark energy component and without addressing the underlying cosmological constant problem. Moreover, all 4D matter sources are geometrically induced in the same manner as it is usually done in the Wesson’s induced matter theory.

The Modern Induced Matter Approach of General Relativity for Quantum Mechanics

Wesson and his co-workers developed so-called space-time-matter theory (5D-STM) as a generalization of Kaluza-Klein theory, where the extra-dimension in the 5D space-time is no more compacted, but keeping extended in a macroscopic scale to describe the properties of matter in 4D physics. In a trend of 5D-STM approach (or the induced-matter theory), following a bi-cylindrical model of geometrical dynamics, a recent study has shown that the higher 6D-dimensional gravitational equation leads to bi-geodesic description in an extended timespace symmetry which fits Hubble expansion in a ”microscopic” cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles. The 4D-embedded dual solutions of the higher dimensional gravitational equation could shed light on origin of physical reality in quantum mechanics, which is to compare with the achievements of the 5D-STM theory.

Gravito-magnetic monopoles in traversable wormholes from WIMT

Abstract Using Weitzenbock Induced Matter Theory (WIMT), we study Schwarzschild wormholes performing different foliations on an extended (non-vacuum) 5D manifold. We explore the geodesic equations for observers which are in the interior of a traversable wormhole and how these observers can detect gravito-magnetic monopoles which are dual to gravito-electric sources observed in the outer zone of some Schwarzschild Black-Hole (BH). The densities of these monopoles are calculated and quantized in the Dirac sense. This kind of duality on the extended Einstein–Maxwell equations, relates electric and magnetic charges on causally disconnected space regions.

Exact cosmological solutions in modified Brans–Dicke theory

In this paper, we obtain exact cosmological vacuum solutions for an extended FLRW homogeneous and isotropic Brans–Dicke (BD) universe in five dimensions for all values of the curvature index. Then, by employing the equations associated with a modified Brans–Dicke theory (MBDT) [], we construct the physics on a four-dimensional hypersurface. We show that the induced matter obeys the equation of state of a fluid of barotropic type. We discuss the properties of such induced matter for some values of the equation of state parameter and analyze in detail their corresponding solutions. To illustrate the cosmological behaviors of the solutions, we contrast our solutions with those of the standard BD theory. We find that, in the MBDT scenario, it is impossible to find a physically acceptable solution associated with the negative curvature for both the dust-dominated and radiation-dominated universes. However, for spatially flat and closed universes, we argue that our obtained solutions are more general than those associated with the standard BD theory and, moreover, they contain a few classes of solutions which have no analog in the BD cosmology. For these particular cases, we further compare the results with those extracted in the context of the induced-matter theory (IMT) and general relativity (GR). Furthermore, we discuss in detail the time behaviors of the cosmological quantities and compare them with recent observational data. We find a favorable range for the deceleration parameter associated with a matter-dominated spatially flat universe (for the late times), which is compatible with recent corresponding observational results.

New effective coupled $$F(^{(4)}\!R,\varphi )$$ F ( ( 4 ) R , φ ) modified gravity from $$f(^{(5)}\!R)$$ f ( ( 5 ) R ) gravity in five dimensions

Using some ideas of the Wesson induced matter theory, we obtain a new kind of $$F(^{(4)}\!R,\varphi )$$ modified gravity theory as an effective four-dimensional (4D) theory derived from $$f(^{(5)}\!R)$$ gravity in five dimensions (5D). This new theory exhibits a different matter coupling than the one in BBHL theory. We show that the field equations of the Wesson induced matter theory and of some brane-world scenarios can be obtained as maximally symmetric solutions of the same $$f(^{(5)}\!R)$$ theory. We found criteria for the Dolgov–Kawasaki instabilities for both the $$f(^{(5)}\!R)$$ and the $$F(^{(4)}\!R,\varphi )$$ theories. We demonstrate that under certain conditions imposed on the 5D geometry it is possible to interpret the $$F(^{(4)}\!R,\varphi )$$ theory as a modified gravity theory with dynamical coefficients, making this new theory a viable candidate to address the present accelerating cosmic expansion issue. Matter sources in the $$F(^{(4)}\!R,\varphi )$$ case appear induced by the 5D geometry without the necessity of the introduction of matter sources in 5D.

Dyonic Reissner-Nordström black hole: extended Dirac quantization from 5D invariants

The aim of present work is to extend the application of Weitzenbock Induced Matter Theory (WIMT) to a dyonic Reissner-Nordstrom Black Hole (RNBH), by proposing a condition compatible with a quantization relation between gravitational mass and both magnetic and electric charges from a geometric product defined as an invariant in 5D.

WIMT in Gullstränd–Painlevé and Reissner–Nordström metrics: induced stable gravito-magnetic monopoles

The aim of this work is to apply Weitzeböck Induced Matter Theory (WIMT) to Gullstränd–Painlevé and Reissner–Nordström metrics in the framework of WIMT. This is a newly developed method that extends Induced Matter Theory from a curved 5D manifold using the Weitzeböck’s geometry, using the fact that the Riemann–Weitzenböck curvature tensor is always null. We obtain the presence of currents whose interpretation can lead to the presence of stable gravito-magnetic monopoles.

Quantized gravito-magnetic charges from WIMT: cosmological consequences

Using the formalism of Weitzenböck induced matter theory (WIMT) we calculate the gravito-magnetic charge on a topological string, which is induced through a foliation on a five-dimensional (5D) gravito-electromagnetic vacuum defined on a 5D Ricci-flat metric, which produces symmetry breaking on an axis. We obtain the resonant result that the quantized charges are induced on the effective four-dimensional hypersurface. This quantization describes the behavior of a test gravito-electric charge in the vicinity of a point gravito-magnetic monopole, both geometrically induced from a 5D vacuum. We demonstrate how gravito-magnetic monopoles would decrease exponentially during the inflationary expansion of the universe.

Matter Confinement Mechanism in de Sitter Brane

The geodesic equation in induced matter theory with de Sitter brane is described. It is shown that the extra forces do not change the four-impulse of massive particles. We also show that the variation of length of the 4-velocity of a test particle in de Sitter brane along the extra dimensions could remain finite resulting in a fluctuating component and hence keeping the particle inside the 4D spacetime and within the observable physics. In fact, the extra components trace closed orbits keep them finite in length. All of these are formulated in the framework of a dynamical system and we characterize the behaviour of the integral curves of this system.

Modified Brans–Dicke theory in arbitrary dimensions

Within an algebraic framework, used to construct the induced-matter-theory (IMT) setting, in (D + 1)-dimensional Brans–Dicke (BD) scenario, we obtain a modified BD theory (MBDT) in D dimensions. Being more specific, from the (D + 1)-dimensional field equations, a D-dimensional BD theory, bearing new features, is extracted by means of a suitable dimensional reduction onto a hypersurface orthogonal to the extra dimension. In particular, the BD scalar field in such D-dimensional theory has a self-interacting potential, which can be suitably interpreted as produced by the extra dimension. Subsequently, as an application to cosmology, we consider an extended spatially flat FLRW geometry in a (D + 1)-dimensional space–time. After obtaining the power-law solutions in the bulk, we proceed to construct the corresponding physics, by means of the induced MBDT procedure, on the D-dimensional hypersurface. We then contrast the resulted solutions (for different phases of the universe) with those usually extracted from the conventional GR and BD theories in view of current ranges for cosmological parameters. We show that the induced perfect fluid background and the induced scalar potential can be employed, within some limits, for describing different epochs of the universe. Finally, we comment on the observational viability of such a model.

DARK ENERGY FROM FIFTH-DIMENSIONAL BRANS–DICKE THEORY

Following the approach of the induced-matter theory, we investigate the cosmological implications of a five-dimensional Brans–Dicke (BD) theory, and propose to explain the acceleration of the universe. After inducing in a four-dimensional hypersurface, we classify the energy–momentum tensor into two parts in a way that, one part represents all kind of the matter (the baryonic and dark) and the other one contains every extra terms emerging from the scale factor of the fifth dimension and the scalar field, which we consider as the energy–momentum tensor of dark energy. We also separate the energy–momentum conservation equation into two conservation equations, one for matter and the other for dark energy. We perform this procedure for different cases, without interacting term and with two particular (suitable) interacting terms between the two parts. By assuming the parameter of the state equation for dark energy to be constant, the equations of the model admit the power-law solutions. Though, the noninteracting case does not give any accelerated universe, but the interacting cases give both decelerated and accelerated universes. For the interacting cases, we figure out analytically the acceptable ranges of some parameters of the model, and also investigate the data analysis to test the model parameter values consistency with the observational data of the distance modulus of 580 SNe Ia compiled in Union2.1. For one of these interacting cases, the best fitted values suggest that BD coupling constant (ω) is ≃ -7.75, however, it also gives the state parameter of dark energy (wX) equal to ≃ -0.67. In addition, the model gives the Hubble and deceleration parameters at the present time to be H◦ ≃ 69.4 (km/s)/Mpc and q◦ ≃ -0.38 (within their confidence intervals), where the scale factor of the fifth dimension shrinks with the time.

Induced Matter Theory of gravity from a Weitzenböck 5D vacuum and pre-big bang collapse of the universe

We extend the Induced Matter Theory of gravity (IMT) to 5D curved spacetimes by using the Weitzenb\"ock representation of connections on a 5D curved spacetime. In this representation the 5D curvature tensor becomes null, so that we can make a static foliation on the extra noncompact coordinate to induce in the Weitzenb\"ock representation the Einstein equations. Once we have done it, we can rewrite the effective 4D Einstein equations in the Levi-Civita representation. This generalization of IMT opens a huge window of possible applications for this theory. A pre-big bang collapsing scenario is explored as an example.

Dirac equation in a de Sitter expansion for massive neutrinos from modern Kaluza–Klein theory

Using the modern Kaluza–Klein theory of gravity (or the Induced Matter theory), we study the Dirac equation for massive neutrinos on a de Sitter background metric from a 5D Riemann-flat (and hence Ricci-flat) extended de Sitter metric, on which is defined the vacuum for test massless 1/2-spin neutral fields minimally coupled to gravity and free of any other interactions. We obtain that the effective 4D masses of the neutrinos can only take three possible values, which are related to the (static) foliation of the fifth and noncompact extra dimension.

Quantum origin of pre-big-bang collapse from induced matter theory of gravity

We revisit a collapsing pre-big-bang model of the universe to study with detail the non-perturbative quantum dynamics of the dispersal scalar field whose dynamics becomes from the dynamical foliation of test massless scalar field φ on a 5D Riemann-flat metric, such that the extra space-like coordinate is noncompact. The important result here obtained is that the evolution of the system, which is described thorough the equation of state has the unique origin in the quantum contributions of the effective 4D scalar field φ¯.