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 the approach of the space-time-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 Λ, or more generally, it may generate a time-dependent cosmological parameter Λ(t). As an application, we construct a simple cosmological model in which Λ(t) has some interesting properties.     

Higher Dimensional Cosmology with Normal Scalar Field and Tachyonic Field

We have considered N-dimensional Einstein field equations in which four-dimensional space-time is described by a FRW metric and that of extra dimensions by an Euclidean metric. We have supposed that the higher dimensional anisotropic universe is filled with only normal scalar field or tachyonic field. Here we have found the nature of potential of normal scalar field or tachyonic field. From graphical representations, we have seen that the potential is always decreases with field φ increases.     

Kaluza-Klein electric monopole in a six-dimensional poincaré gauge theory of gravitation

We found a solution to the six-dimensional Poincaré gauge theory that can be interpreted as the gravitational field and the electric field of an electric monopole in four-dimensional spacetime. The extra dimensions are curled up into a compact space of a size characterized by the Planck length.     

The G2 invariant compactifications in eleven-dimensional supergravity

In this article we study the most general compactifications of eleven-dimensional supergravity to four-dimensional anti-de Sitter space, using a seven-dimensional internal compact manifold whose local isometry group contains the exceptional group, G₂. We find that the only such compactifications are the well known ones involving the round seven-sphere. We discuss the implications of this result for conjectured relationship between the eleven-dimensional theory and gauged N = 8 supergravity.     

Consistent ADD scenario with stabilized extra dimension

A model with one compact extra dimension and a scalar field of Brans–Dicke type in the bulk is discussed. It describes two branes with non-zero tension embedded into the space-time with flat background. This setup allows one to use a very simple method for stabilization of the size of extra dimension. It appears that the four-dimensional Planck mass is expressed only through parameters of the scalar field potentials on the branes.     

Kaluza-Klein black hole in a six-dimensional Poincaré gauge theory of gravitation

We found a solution to the six-dimensional Poincaré gauge theory which can be interpreted as the exterior gravitational field of an uncharged black hole in the four-dimensional spacetime. The extra dimensions are curled up into a compact space of the size characterized by the Planck length.     

Properties of the Higgs particle in a model involving a single unified fermion generation

The properties of the Higgs boson are studied within a model where three generations of Standard Model fermions emerge from one generation in a theory featuring two extra spatial dimensions. It is shown that, despite a nontrivial external field forming a brane, the interactions of the Higgs particle in the effective four-dimensional theory are virtually identical to the interactions of this particle in the Standard Model. Arguments in favor of the statement that the Higgs boson must be rather light in the model being considered are also presented.     

Cosmic Entropy from the Bosonic String?

In Kaluza-Klein models, the compactification ofa high number of extra spatial dimensions generatesentropy in the observable four-dimensional universe. AKaluza–Klein cosmological model recently derived from the bosonic string theory in the limit ofan infinite number of extra dimensions is compared withthe available data from the observations of cosmicmicrowave background anisotropies.     

Non-gravitating scalars and spacetime compactification

We discuss role of partially gravitating scalar fields, scalar fields whose energy–momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits a factorizable geometry consisting of usual four-dimensional spacetime with full Poincaré invariance times a manifold of extra dimensions whose size and shape are determined by the scalar field dynamics. Depending on the strength of its coupling to the curvature scalar, the vacuum expectation value (VEV) of the scalar field may or may not vanish. When its VEV is zero the higher-dimensional spacetime is completely flat and there is no compactification effect at all. On the other hand, when its VEV is nonzero the extra dimensions get spontaneously compactified. The compactification process is such that a bulk cosmological constant is utilized for curving the extra dimensions.     

The structure of groups of motions admitted by Einstein-Maxwell space-times

The known symmetry of the non-null electromagnetic field, which acts as the source of a four-dimensional space-time satisfying the Einstein-Maxwell equations, is used to show that when such a space-time admits a group of motions, generated by a Killing vector, the structure constants for the group must satisfy an additional relation to the known relations of group theory.     

Heterotic and Type I string dynamics from eleven dimensions

We propose that the ten-dimensional E₈ × E₈ heterotic string is related to an eleven-dimensional theory on the orbifold in the same way that the Type IIA string in ten dimensions is related to . This in particular determines the strong coupling behavior of the ten-dimensional E₈ × E₈ theory. It also leads to a plausible scenario whereby duality between SO(32) heterotic and Type I superstrings follows from the classical symmetries of the eleven-dimensional world, just as the duality of the ten-dimensional Type IIB theory follows from eleven-dimensional diffeomorphism invariance.     

The existence of the: exp ϕ:4 quantum field theory in a finite volume

The quantum field theory with an exponential interaction in the four-dimensional space-time in a periodic box is considered. It is shown that the vacuum expectation values exist as tempered distributions and satisfy some Wightman axioms.     

Higher Dimensional Cosmology with Some Dark Energy Models in Emergent, Logamediate and Intermediate Scenarios of the Universe

We have considered N-dimensional Einstein field equations in which four-dimensional space-time is described by a FRW metric and that of extra dimensions by an Euclidean metric. We have chosen the exponential forms of scale factors a and d numbers of b in such a way that there is no singularity for evolution of the higher dimensional Universe. We have supposed that the Universe is filled with K-essence, Tachyonic, Normal Scalar Field and DBI-essence. Here we have found the nature of potential of different scalar field and graphically analyzed the potentials and the fields for three scenario namely Emergent Scenario, Logamediate Scenario and Intermediate Scenario. Also graphically we have depicted the geometrical parameters named statefinder parameters and slow-roll parameters in the higher dimensional cosmology with the above mentioned scenarios.     

Riccion from higher-dimensional space-time with D-dimensional sphere as a compact manifold and one-loop renormalization

Lagrangian density of riccions is obtained with the quartic self-interacting potential using higher-derivative gravitational action in (4 +D)-dimensional space-time withS ^D as a compact manifold. It is found that the resulting four-dimensional theory for riccions is one-loop multiplicatively renormalizable. Renormalization group equations are solved and its solutions yield many interesting results such as (i) dependence of extra dimensions on the enegy mass scale showing that these dimensions increase with the increasing mass scale up toD = 6, (ii) phase transition at 3.05 × 10¹⁶ GeV and (iii) dependence of gravitational and other coupling constants on energy scale. Results also suggest that space-time above 3.05 × 10¹⁶ GeV should be fractal. Moreover, dimension of the compact manifold decreases with the decreasing energy mass scale such thatD = 1 at the scale of the phase transition. Results imply invisiblity of S¹ at this scale (which is 3.05 × 10¹⁶ GeV).     

Grand unification at intermediate mass scales through extra dimensions

One of the drawbacks of conventional grand unification scenarios has been that the unification scale is too high to permit direct exploration. In this paper, we show that the unification scale can be significantly lowered (perhaps even to the TeV scale) through the appearance of extra space-time dimensions. Such extra dimensions are a natural consequence of string theories with large-radius compactifications. We show that extra space-time dimensions naturally lead to gauge coupling unification at intermediate mass scales, and moreover may provide a natural mechanism for explaining the fermion mass hierarchy by permitting the fermion masses to evolve with a power-law dependence on the mass scale. We also show that proton-decay constraints may be satisfied in our scenario due to the higher-dimensional cancellation of proton-decay amplitudes to all orders in perturbation theory. Finally, we extend these results by considering theories without supersymmetry; experimental collider signatures; and embeddings into string theory. The latter also enables us to develop several novel methods of explaining the fermion mass hierarchy via D-branes. Our results therefore suggest a new approach towards understanding the physics of grand unification as well as the phenomenology of large-radius string compactifications.     

Quantum effects on higher dimensional space-time

Particle production in an odd-dimensional homogeneous universe with small anisotropy is discussed by using the effective action method. The pair production is a completely non-local phenomenon in an odd-dimensional theory, in contrast to the case of the familiar four-dimensional space-time. The effect of the closedness of the extra-dimensional space, i.e., the Casimir effect, which seems to be important in the scenario of Kaluza-Klein cosmology, is also discussed in the case of five dimensions.     

Weak gravity conjecture with large extra dimensions

In the presence of large extra dimensions, the fundamental Planck scale can be much lower than the apparent four-dimensional Planck scale. In this setup, the weak gravity conjecture implies a much more stringent constraint on the UV cutoff for the U(1) gauge theory in four dimensions. This new energy scale may be relevant to LHC.     

Orbifold compactification and solutions of M-theory from Milne spaces

In this paper, we consider solutions and spectral functions of M-theory from Milne spaces with extra free dimensions. Conformal deformations to the metric associated with real hyperbolic space forms are derived. For the three-dimensional case, the orbifold identifications , where Id is the identity matrix, is analyzed in detail. The spectrum of an eleven-dimensional field theory can be obtained with the help of the theory of harmonic functions in the fundamental domain of this group and it is associated with the cusp forms and the Eisenstein series. The supersymmetry surviving for supergravity solutions involving real hyperbolic space factors is briefly discussed.Received: 30 November 2004, Published online: 25 January 2005     

On superplanckian scattering on the brane

The multidimensional space-time with (D-4) compact extra space dimensions and SM fields confined on a four-dimensional brane is considered. The elastic scattering amplitude of two particles interacting by gravitational forces is calculated at superplanckian energies. Particular attention is paid to a proper account of zero (massless) graviton mode. The renormalized Born pole is reproduced in the eikonal amplitude which makes a leading contribution at small momentum transfers. This singular part of the amplitude coincides with well-known D-dimensional amplitude taken at . The expression for the contribution from massive graviton modes to the eikonal is derived, and its asymptotics in the impact parameter is calculated. Our formula gives the correct four-dimensional expression at , where R_c is the radius of the higher dimensions. The results are also compared with those obtained previously for the scattering of the bulk fields in flat extra dimensions.Received: 9 September 2003, Revised: 2 February 2004, Published online: 2 April 2004