Affine Metrics: An Structure for Unification of?Gravitation and Electromagnetism

This paper is mainly intended to define a mathematical framework for unification of gravity and electromagnetism. The main idea is that affine concepts replace linear concepts in the context of general relativity. First, we introduce affine metrics on affine spaces,and then generalize semi-Riemannian manifolds to affine semi-Riemannian manifolds and investigate their associated connections and geodesics and curvatures. Then we apply these concepts to space-times in order to combine Maxwell’s and Einstein’s field equations into one equation.     

Born’s Reciprocal Gravity in Curved Phase-Spaces and the Cosmological Constant

The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the construction of the curvature of the 8D cotangent space and based on the (torsionless) Levi-Civita connection is provided that yields the observed value of the cosmological constant and the Brans-Dicke-Jordan Gravity action in 4D as two special cases. It is found that the geometry of the momentum space can be linked to the observed value of the cosmological constant when the curvature in space is very large, namely the small size of P is of the order of . Finally we develop a Born’s reciprocal complex gravitational theory as a local gauge theory in 8D of the Quaplectic group that is given by the semi-direct product of U(1,3) with the (noncommutative) Weyl-Heisenberg group involving four coordinates and momenta. The metric is complex with symmetric real components and antisymmetric imaginary ones. An action in 8D involving 2 curvature scalars and torsion squared terms is presented.     

String Cosmological Solutions in Self-Creation Theory of Gravitation

We have studied the problem of cosmic strings for Bianchi-I, II, VIII and IX string cosmological models in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) second self—creation theory of gravitation. We have obtained some classes of solutions by considering different functional form for metric potentials. It is also observed that due to the presence of scalar field, the power index ‘m’ of the metric coefficients has a range of values.     

Bulk Viscous Bianchi Type-V Cosmological Models with Variable Gravitational and Cosmological Constant

This paper deals with Bianchi type-V cosmological models of the universe filled with a bulk viscous cosmic fluid in the framework of general relativity. A new class of exact solutions has been obtained by considering various well established power law relations among scale factor, cosmological and gravitational constants and cosmic time. Some physical and geometrical behaviors of the models have also been discussed. It has been found that all the models are in fair agreement of observational results.     

A Higher Dimensional Cosmological Model in a Scale-Covariant Theory of Gravitation

Kaluza-Klein space-time is considered in the presence of a perfect fluid distribution in the scale-covariant theory of gravitation by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983), a cosmological model in five dimensions with a negative constant deceleration parameter is presented in this theory. Some physical and kinematical properties of the model are also discussed.     

New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity

In this work, we apply the anholonomic deformation method for constructing new classes of anisotropic cosmological solutions in Einstein gravity and/or generalizations with nonholonomic variables. There are analyzed four types of, in general, inhomogeneous metrics, defined with respect to anholonomic frames and their main geometric properties. Such spacetimes contain as particular cases certain conformal and/or frame transforms of the well known Friedman-Robertson-Walker, Bianchi, Kasner and Gödel universes and define a great variety of cosmological models with generic off-diagonal metrics, local anisotropy and inhomogeneity. It is shown that certain nonholonomic gravitational configurations may mimic de Sitter like inflation scenarios and different anisotropic modifications without satisfying any classical false-vacuum equation of state. Finally, we speculate on perspectives when such off-diagonal solutions can be related to dark energy and dark matter problems in modern cosmology.     

Bianchi Type-III Cosmological Models with Gravitational Constant G and the Cosmological Constant ∧

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-Ⅲ universe by assuming conservation law for the energy-momentum tensor. Exact solutions of the field equations are obtained by using the scalar of expansion proportional to the shear scalar θ∝σ, which leads to a relation between metric potential B = Cn, where n is a constant. The corresponding physical interpretation of the cosmological solutions are also discussed.     

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.     

Anisotropic Plane Symmetric Magnetized Model with Cosmological Constant

In this paper, we have obtained the solutions of perfect fluid cosmological model in Cylindrically-symmetric space time (Marder in Proc. R. Soc. A 246:133, 1958) with varying cosmological constant in the presence of electromagnetic field. To get determinate model of the universe we assumed that the scalar of expansion in the model is proportional to the eigen-value of the shear tensor which lead to the condition A=(BC) ⁿ . The magnetic field is due to an electric current produced along x-axis. Thus the magnetic field is in yz-plane and F ₂₃ is the only non-vanishing component of electromagnetic field tensor F _ij . Various physical and geometrical features of the model have been discussed.     

Scale Transformation,Modified Gravity,and Brans-Dicke Theory

A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in f(R) metric formalism nor the ones in f(ℛ) Palatini formalism, whereas the modified source terms are formally equivalent to those of f(R)=\frac12R²f({\mathcal{R}})=\frac{1}{2}{\mathcal{R}}^{2} gravity in Palatini formalism. The correspondence between the present model, the modified gravity theory, and Brans-Dicke theory with w = -\frac32\omega=-\frac{3}{2} is explicitly shown, provided the dilaton field is condensated to its vacuum state.     

Separation of Spin 0, 1/2, 1 Field Equations in Lemaître-Tolman-Bondi Cosmological Model with Cosmological Constant

The problem of variable separation of the scalar field equation is approached within the Lemaître-Tolman-Bondi (LTB) cosmological model with cosmological constant Λ. Parametric solutions of the cosmological Newton-like equation of the model are preliminary determined that result factorized in the parameter and in the radial dependence. The result holds on a sufficient condition that relates the two arbitrary integration functions of the model. The condition is of the same type of the one that ensures, in absence of cosmological term, the separability of the spin field equations for spin 0, 1/2, 1. It is then shown that the scalar field equation results automatically separable in the class of LTB models determined. The separated radial equation results independent of Λ, while the separated time equation strictly depends on Λ. The separability of the field equations is then checked to hold, in the same context, for spinor field equation of spin 1/2 and spin 1.     

Immeasurability of Zero-Point Energy in?the?Cosmological Constant Problem

A huge discrepancy between the zero-point energy calculated from quantum theory and the observed quantity in the Universe has been one of the most illusive problems in physics. In order to examine the measurability of zero-point energy, we construct reference frames in a given measurement using observables. Careful and explicit construction of the reference frames surprisingly reveals that not only is the harmonic oscillator fluctuating at the ground level, but so is the reference frame when the measurement is realized. The argument is then extended to examine the measurability of vacuum energy for a quantized electromagnetic field, and it is shown that while zero-point energy calculated from quantum theory diverges to infinity, it is not measurable.     

Cosmological constant in a model with superstring-inspired E 6 unification and shadow θ-particles

We have developed the concept of parallel existence of the ordinary (O-) and mirror (M-), or shadow (Sh-) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking E ₆→SU(3)³ in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. E ₆ unification, inspired by superstring theory, restores the broken mirror parity at the scale ～10¹⁸ GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: E ₆→SO(10)×U(1) _Z in the O-world, and E′₆→SU(6)′×SU(2)′ _θ in the Sh-world. We assume the existence of shadow θ-particles and the low-energy symmetry group SU(3)′ _C ×SU(2)′ _L ×SU(2)′ _θ ×U(1)′ _Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)′ _θ group with massless gauge fields, “thetons”, has a macroscopic confinement radius 1/Λ′ _θ . The assumption that Λ′ _θ ≈2.3?10^?3 eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as E ₆, from cosmology.     

Scaling Law for the Cosmological Constant from Quantum Cosmology with Seven Extra Dimensions

According to a model of quantum cosmology the maximum number of degrees of freedom allowed in our three dimensions was determined by the size of seven extra dimensions in an initial excited state before inflation. The size of the extra dimensions can be inferred from a simple scheme for unifying the strong force and gravity. Coupled with the Bekenstein-Hawking entropy bound, these considerations lead to a scaling law for the cosmological constant that has been proposed independently by several authors.     

Cosmological evolution of interacting dark energy in Lorentz violation

The cosmological evolution of an interacting scalar-field model in which the scalar field interacts with dark matter, radiation, and baryons via Lorentz violation is investigated. We propose a model of interaction through the effective coupling, [`(b)]\bar{\beta} . Using dynamical system analysis, we study the linear dynamics of an interacting model and show that the dynamics of critical points are completely controlled by two parameters. Some results can be mentioned as follows. Firstly, the sequence of radiation, the dark matter, and the scalar-field dark energy exist and baryons are subdominant. Secondly, the model also allows for the possibility of having a universe in the phantom phase with constant potential. Thirdly, the effective gravitational constant varies with respect to time through [`(b)]\bar{\beta} . In particular, we consider the simple case where [`(b)]\bar{\beta} has a quadratic form and has a good agreement with the modified ΛCDM and quintessence models. Finally, we also calculate the first post-Newtonian parameters for our model.     

Phase Transitions in the Early Universe with Negatively Induced Supergravity Cosmological Constant

We consider that the observable cosmological constant is the sum of the vacuum （Avac） and the induced term （Aind - 3m^2/4） with m being the ultra-llght masses （≈ Hubble parameter） implemented in the theory from supergravities arguments and non-minimal coupling. In the absence of a scalar buildup of matter fields, we study its effects on spontaneous symmetry breaking with a Higgs potential and show how the presence of the ultra-light masses yields some important consequences for the early universe and new constraints on the Higgs and electroweak gauge bosons masses.     

Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo-Finsler/Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions with regular rotating event horizon. For corresponding parameterizations, the metrics and connections define Finsler–Einstein geometries modeled on tangent bundles, or on nonholonomic (pseudo) Riemannian manifolds. In general, there are vacuum nonholonomic gravitational configurations which can not be generated in the limit of zero cosmological constant.     

Magnetized Domain Walls Cosmological Model in General Relativity

A non-static Bianchi type-III domain walls cosmological models in presence and absence of magnetic field are investigated in general theory of relativity. We assume that F ₁₂ is only the non-vanishing component of F _ij . To obtain deterministic model, we assume relations B=C ⁿ and ρ=p. Some physical properties of these models are discussed.     

A Higher Dimensional Cosmic Domain Wall in Brans-Dicke Theory of Gravitation

Five dimensional Kaluza-Klein Space-time is considered in the presence of thick domain walls in the scalar-tensor theory formulated by Brans and Dicke (Phys. Rev. 124:925, 1961). Exact cosmological model, in this theory, is presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983) for Hubble’s parameter. Some physical and kinematical properties of the model are also discussed.     

Neutrino Mixing Matrix and Leptogenesis from Quantum Gravity

We consider non renormalization 1/M _x interaction term as a perturbation of the neutrino mass matrix. We find that for the degenerate neutrino mass spectrum. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. We also assume, above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bimaximal. The perturbation generates a non zero value of θ ₁₃, which is within reach of the high performance neutrino factory. In this paper, we find that the non zero value of θ ₁₃ due to Planck scale effects indicates the possibility of CP violation.