A universe embedded in a five-dimensional flat space

Since a homogeneous isotropic universe can be embedded in a flat space of five dimensions, the question is considered under what conditions a more general universe can be embedded in a five-dimensional flat space. On the assumption that the deviation from homogeneity is small, it is found that real inhomogeneities can occur only in the case of a universe filled with radiation, or a universe containing at least two different substances with different equations of state, as for example radiation and matter. In the case of a radiation-filled universe, the inhomogeneities can be of arbitrary size and can conceivably be the precursors of galaxies.     

Prolegomena to a theory of bifurcating universes: A nonlocal solution to the cosmological constant problem or little lambda goes back to the future

We outline a framework for describing the bifurcation of the universe into disconnected pieces, and formulate criteria for a system in which such phenomena occur, to describe local quantum physics in a single connected universe. The formalism is a four-dimensional analog of string field theory which we call Universal Field Theory (UFT). We argue that local dynamics in a single universe is a good approximation to UFT if the universal field is classical and if the vertex for emission of a new connected component of the universe is concentrated on universes of small volume. We show that classical UFT is equivalent to a Wheeler-DeWitt equation for a single connected universe plus a set of nonlocal gap equations for the couplings in the spacetime lagrangian. The effective action must be stationary with respect to the couplings. Nonlicality shoes up only at short distances. We solve the equation for the low-energy cosmological constant and show that if the universe undergoes substantial inflation then the cosmological constant is determined to be negative and very small. Its precise value may depend on the fate of nonrelativistic matter in the very late stages of universal expansion. Finally, we argue that corrections to the classical UFT are nonlocal and must be suppressed if the theory is to make sense. This may be the reason that supersymmetric vacua of string theory are not realized in nature.     

Numerical evolution,linear and nonlinear,of spherically symmetric deviations from an isotropic universe

We describe an algorithm for solving 1 + 1-systems that are in symmetric hyperbolic form. It is applied to spherically symmetric deviations from ak = 0, radiation filled Isotropic universe. We compare the solution to the full Einstein equations with those of the linearized equations. For small enough initial data the evolutions are indistinguishable. However, for large data, i.e., for initial density contrasts in the 1 percent range, trapped surfaces appear and singularities form.     

Curvature in causal BD-type inflationary cosmology

We study a closed model of the universe filled with viscous fluid and quintessence matter components in a Brans-Dicke type cosmological model. The dynamical equations imply that the universe may look like an accelerated flat Friedmann-Robertson-Walker universe at low redshift. We consider here dissipative processes which follow a causal thermodynamics. The theory is applied to viscous fluid inflation, where accepted values for the total entropy in the observable universe are obtained.     

Radiating Kerr particle in Einstein universe

A generalized Kerr-NUT type metric is considered in connection with Einstein field equations corresponding to perfect fluid plus a pure radiation field. A general scheme for obtaining the exact solutions of these field equations is developed. Two physically meaningful particular cases are investigated in detail. One gives the field of a radiating Kerr particle embedded in the Einstein universe. The other solution may probably represent a deSitter-like universe pervaded by a pure radiation field.     

Remarks on the Idea of Spontaneous Break-Down of Symmetry,Cosmic Variability of Eddington's Number,Mach's Idea Concering the Origin of Inertia,and Field Equations Describing Global and Local Gravitational Fields

Subject is considered on the level of classical field theory. We start from some aspects of the theory of ferromagnets. Their counterpart in classical field theory is pointed out using the over simplified model of a selfinteracting scalar field. The ground state (“vacuum expection value”) of the scalar field is interpreted as cosmic background field, which can be considered as constant for local physical phenomena. In practice, however, it is a function of the age of universe. Which kind of function it could be is suggested by a discussion of the cosmic variability of Eddington's number γ = 10⁴⁰, which refers to Dirac's consideration of this problem. But contrary to Dirac's assumption that atomic quantities are constant, we suppose that the inertial mass of elementary particles is a function of the age of universe. The cosmic gravitational field is described by other equations than the gravitational field created by local matter distributions. The field equations for the local gravitational field we start from reduce to Einstein's equations, if we neglect the possible influence of the universe on local phenomena. In case that the cosmic matter is homogeneously and isotropically distributed, the field equations for the cosmic gravitational field permit only such a time dependent solution the three-spaces of which are linearly expanding and spherically closed. The different field equations for cosmic and local gravitational fields are considered approximations of more fundamental field equations which approximately split into two sets of equations, if it is possible to contrast local physical systems with the universe. The described cosmological model taken as a basis, the inertial mass of elementary particles becomes a function of the matter density creating the cosmic gravitational field. This could be considered as, at least, partly realisation of Mach's idea concerning the origin of inertia. Starting from the interpretation of the ground state (vacuum expection value) as a function of a certain cosmic background field, more realistic gage field models could give the following picture of cosmic development: In the far past there was a state of the universe characterized by enormous contraction of matter. In this stage of development, it was impossible to contrast particles with the universe. Matter expands and it becomes possible to contrast certain physical systems with the universe. But the ground state is such a symmetric one that only fields with vanishing rest mass can be contrasted with the universe (ferromagnet above Curie temperature). With further expansion of the universe the ground state will lose certain symmetry properties. By this it becomes possible that you get the impression there are particles with nonvanishing rest mass (ferromagnet below Curie temperature). Finally, the influence of the universe on local physical systems goes to zero with further expansion. Especially, this means the inertial mass of elementary particles goes to zero, too (Curie temperature of ferromagnetic material goes to zero with cosmic expansion).     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann-Robertson-Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi(LTB) cosmology supported by a perfect Suid source.This model is the natural generalization of the Sat Friedmann-Robertson-Walker(FRW) universe,and describes an inhomogeneous universe with spherical symmetry.After reviewing some basic equations in the parabolic LTB cosmology,we obtain a relation for the deceleration parameter in this model.We also obtain a condition for which the universe undergoes an accelerating phase at the present time.We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology.We find out that in LTB model of cosmology,the apparent horizon's entropy could be feeded by a term,which incorporates the effects of the inhomogeneity.We consider this result and get a relation for the total entropy evolution,which is used to examine the generalized second law of thermodynamics for an accelerating universe.We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Quantum cosmology in 2+1 and 3+1 dimensions

We study the Wheeler-DeWitt equations for the wave function of the universe in 2+1 and 3+1 dimensions. Perturbation methods are developed and the first few orders areexplicitly calculated for the case of an inflating universe. We find that early quantum fluctuation can produce large-scale inhomogenities in the global structure of the universe at later times.     

Anisotropic Bianchi-I universe with phantom field and cosmological constant

We study an anisotropic Bianchi-I universe in the presence of a phantom field and a cosmological constant. Cosmological solutions are obtained when the kinetic energy of the phantom field is of the order of anisotropy and dominates over the potential energy of the field. The anisotropy of the universe decreases and the universe transits to an isotropic flat FRW universe accommodating the present acceleration. A class of new cosmological solutions is obtained for an anisotropic universe in case an initial anisotropy exists which is bigger than the value determined by the parameter of the kinetic part of the field. Later, an autonomous system of equations for an axially symmetric Bianchi-I universe with phantom field in an exponential potential is studied. We discuss the stability of the cosmological solutions.      

Brans-Dicke cosmological exact solution in a radiation-filled Robertson-Walker universe

In a recent paper Singh and Deo obtained the field equations in Brans-Dicke theory for a radiation-filled universe with Robertson-Walker metric and solved the equations for a particular case. Here we obtain the complete set of solutions of these equations.     

Cosmological solutions for the coupled Einstein-Yang-Mills-Higgs equations

The coupled system of Einstein-Yang-Mills-Higgs equations is solved numerically for a Robertson-Walker symmetric universe. The open universe must be excluded because, for this situation, the coupled system is unable to produce energy-momentum densityT in agreement with the Robertson-Walker symmetry. For the closed universe, inflation solutions do occur if an early re-collapse is avoided by suitable choice of the initial conditions. The energy exchange between the minimally coupled Higgs and Yang-Mills subsystems is very small so that the inflating power of the Higgs field cannot be disturbed by the presence of the Yang-Mills field. After the inflation phase the influence of the Yang-Mills field is completely negligible (cosmic no-hair theorem).     

Anisotropic Bianchi Type-II Massive String Cosmological Models with Time-Decaying Λ Term and Thermodynamic Parameters

The present paper envisages a spatially homogeneous and anisotropic Bianchi II massive string cosmological models with time-decaying Λ term in general relativity. By using the variation law of Hubble’s parameter, the Einstein’s field equations have been solved for two general cases. The first case involving a power law solution describes the dynamics of universe from big bang to present epoch while the second case admit an exponential solution seems reasonable to project dynamics of future universe. We observed that massive strings dominate in early universe and eventually disappear at late time, which is consistent with the current astronomical observations. It has been found that the cosmological constant (Λ) is a decreasing function of time and it approaches to small positive value at sufficiently large time. The thermodynamic properties of anisotropic Bianchi II universe are studied and also the absolute temperature and entropy distribution are given explicitly. The relations between thermodynamic parameters and cosmological constant Λ has been established. Physical behavior of the derived model is elaborated in detail.     

Cosmological Model Based on Gauge Theory of Gravity

A cosmological model based on gauge theory of gravity is proposed in this paper. Combining cosmological principle and field equation of gravitational gauge field, dynamical equations of the scale factor R(t) of our universe can be obtained. This set of equations has three different solutions. A prediction of the present model is that, if the energy density of the universe is not zero and the universe is expanding, the universe must be space-flat, the total energy density must be the critical density ρ_c of the universe. For space-flat case, this model gives the same solution as that of the Friedmann model. In other words, though they have different dynamics of gravitational interactions, general relativity and gauge theory of gravity give the same cosmological model.     

Bulk Viscous Bianchi Type-III Cosmological Model with Time-Dependent <Emphasis Type="Italic">G</Emphasis> and Λ

This paper deals with Bianchi type-III anisotropic cosmological model of the universe filled with a bulk viscous fluid with time varying gravitational and cosmological constants. It is shown that the field equations are solvable for any arbitrary cosmic scale function. Exact solutions of Einstein’s field equations are obtained which represent an expanding, shearing, non-rotating and decelerating universe. The physical behaviour of the model has also been discussed.     

Fermions and expanding universe

The coupledDirac-Einstein equations for a homogeneous isotropic space-time forbid aclosed universe but lead to the standard cosmological model for aflat universe. Therefore only theopen universe is left as a nontrivial situation. There some of the desired cosmological effects emerge in a natural way:inflation, creation ex nihilo, etc.     

Stochastic evolution of cosmological parameters in the early universe

We develop a stochastic formulation of cosmology in the early universe, after considering the scatter in the redshift-apparent magnitude diagram in the early epochs as an observational evidence for the non-deterministic evolution of early universe. We consider the stochastic evolution of density parameter in the early universe after the inflationary phase qualitatively, under the assumption of fluctuating w factor in the equation of state, in the Fokker-Planck formalism. Since the scale factor for the universe depends on the energy density, from the coupled Friedmann equations we calculated the two variable probability distribution function assuming a flat space geometry.     

Eine kosmologische Lösung der TREDERschen Gravitationstheorie

A solution of the field equations is given for the case of an universe filled with incoherent matter (p = 0). The observable universe behaves kinematically in a good approximation like the MILNE -model but with flat subspaces t = const.     

On the stability of the Taub universe

An analysis of the stability of the Taub universe for arbitrary, initially small perturbations is carried out. It is found that the perturbations decrease during the expansion and increase during the contraction of the unperturbed space. In the process we obtain the general solution to a system of six coupled, linear, partial differential equations in six unknown functions of four variables.This work will be presented as a thesis to the Department of Physics, University of Chicago, in partial fulfillment of the requirements for the Ph. D. degree.     

Friedmann-Like Equations for High Energy Area of Universe

In this paper, evolution of the high energy area of universe, through the scenario of 5 dimensional (5D) universe, has been studied. For this purpose, we solve Einstein equations for 5D metric and 5D perfect fluid to derive Friedmann-like equations. Then we obtain the evolution of scale factor and energy density with respect to both space-like and time-like extra dimensions. We obtain the novel equations for the space-like extra dimension and show that the matter with zero pressure cannot exist in the bulk. Also, for dark energy fluid and vacuum fluid, we have both accelerated expansion and contraction in the bulk.