Tilted homogeneous cosmological models

We examine spatially homogeneous cosmological models in which the matter content of space-time is a perfect fluid, and in which the fluid flow vector is not normal to the surfaces of homogeneity. In such universes, the matter may move with non-zero expansion, rotation and shear; we examine the relation between these kinematic quantities and the Bianchi classification of the symmetry group. Detailed characterizations of some of the simplest such universe models are given.     

Electric charge in the Kruskal space-time and the Jeans conjecture

In 1928 Jeans conjectured that there might be regions in space such as for example centers of galaxies through which matter could be flowing into our universe from other universes. We investigate if this conjecture extended to charged matter could be realized within the framework of general relativity with the help of black and white holes. By studying a test electromagnetic field produced by a point charge in the maximally extended Schwarzschild space-time we show that an observer at infinity always can get an information on the value of the charge even if it is hidden inside a white hole. Therefore we conclude that the Jeans conjecture cannot be realized for charged matter by a white hole. This result can be generalized to include a test gravitational field produced by a test mass hidden inside a white hole, hole.On leave from Institute of Theoretical Physics, University of Warsaw, Warsaw, Poland.     

Some remarks on nonlocal field theory and space-time quantization

From the point of view that the charge and mass of an electron is of dynamical origin and quantization of charge in units ofe is related to the space-time quantization as developed in an earlier paper, we here show that it is possible to consider that the internal space within the elementary domain of the quantized space-time world is not governed by Lorentz invariance. This helps us to develop a consistent theory of nonlocal fields for extended particles where the infinite mass degeneracy is avoided. Moreover, this ensures the convergence of nonlocal field theories and suggests that massless particles like photons and neutrinos, though they may be taken to be of extended structure, will appear only as point particles in the physical world. In this picture, Lorentz invariance appears to be a consequence of the distribution of matter and energy in the Universe, and this may be taken to be another interpretation of Mach's principle.     

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville integrable system. For the determination of the conservation laws we apply the Cartan symmetries. Furthermore, inspired from our solutions, a toy model is studied and it is shown that it can describe the Supernova data, while at the same time introduces dark matter components in the Hubble function. When the extra matter source is a stiff fluid then we show how analytical solutions for Bianchi I universes can be constructed from our analysis. Finally, we perform a global dynamical analysis of the field equations by using variables different from that of the Hubble-normalization.     

Was the big bang a whimper?

In many cases the spatially homogeneous cosmological models of General Relativity begin or end at a “big bang” where the density and temperature of the matter in the universe diverge. However in certain cases the spatially homogeneous development of these universes terminates at a singularity where all physical quantities are well—behaved (a “whimper”) and an associated Cauchy horizon. We examine the existence and nature of these singularities, and the possible fate of matter which crosses the Cauchy horizon in such a universe. The nature of both kinds of singularity is illustrated by simple models based on two-dimensional Minkowski space-time; and the possibility of other types of singularity occuring is considered.     

Quantum entanglement in the multiverse

We show that the quantum state of a multiverse made up of classically disconnected regions of the space-time, whose dynamical evolution is dominated by a homogeneous and isotropic fluid, is given by a squeezed state. These are typical quantum states that have no classical counterpart and therefore allow analyzing the violation of classical inequalities as well as the EPR argument in the context of the quantum multiverse. The thermodynamical properties of entanglement are calculated for a composite quantum state of two universes whose states are quantum-mechanically correlated. The energy of entanglement between the positive and negative modes of a scalar field, which correspond to the expanding and contracting branches of a phantom universe, are also computed.     

Reconstruction of the equation of state for the cyclic universes in homogeneous and isotropic cosmology

We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) space-time. In particular, we reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic functions. It is explicitly illustrated that in several models the universe always stays in the non-phantom (quintessence) phase, whereas there also exist models in which the crossing of the phantom divide can be realized in the reconstructed cyclic universes.     

Singularities in Bianchi cosmologies

We discuss how infinite density singularities may be shown to occur in Friedmann-Robertson-Walker universes and orthogonal spatially homogeneous universes, but how very different behaviours are possible in tilted homogeneous cosmologies. After considering various possibilities that arise in this case, we illustrate them by examining the behaviour of exact solutions of Einstein's equations for a homogeneous cosmology which is a locally rotationally symmetric tilted Bianchi type V universe. These universes - which can be arbitrarily similar to a Robertson-Walker universe at late times - show a variety of singular behaviours quite different from those in the ‘orthogonal’ case. In particular, there exist such universes in which two singularities occur at the early stages of the universe, but in which the density of matter is finite at all times.     

Implications of a stochastic microscopic Finsler cosmology

Within the context of supersymmetric space-time (D-particle) foam in string/brane-theory, we discuss a Finsler-induced cosmology and its implications for (thermal) dark matter abundances. This constitutes a truly microscopic model of dynamical space-time, where Finsler geometries arise naturally. The D-particle foam model involves point-like brane defects (D-particles), which provide the topologically non-trivial foamy structures of space-time. The D-particles can capture and emit stringy matter and this leads to a recoil of D-particles. It is indicated how one effect of such a recoil of D-particles is a back-reaction on the space-time metric of Finsler type which is stochastic. We show that such a type of stochastic space-time foam can lead to acceptable cosmologies at late epochs of the Universe, due to the non-trivial properties of the supersymmetric (BPS like) D-particle defects, which are such so as not to affect significantly the Hubble expansion. The restrictions placed on the free parameters of the Finsler type metric are obtained from solving the Boltzmann equation in this background for relic abundances of a Lightest Supersymmetric Particle (LSP) dark matter candidate. It is demonstrated that the D-foam acts as a source for particle production in the Boltzmann equation, thereby leading to enhanced thermal LSP relic abundances relative to those in the Standard ??CDM cosmology. For D-particle masses of order TeV, such effects may be relevant for dark matter searches at colliders. The latter constraints complement those coming from high-energy gamma-ray astronomy on the induced vacuum refractive index that D-foam models entail. We also comment briefly on the production mechanisms of such TeV-mass stringy defects at colliders, which, in view of the current LHC experimental searches, will impose further constraints on their couplings.     

Bianchi Type-II, VIII & IX Cosmological Models with Strange Quark Matter Attached to String Cloud in Brans–Dicke and General Theory of Gravitation

We have obtained and presented spatially homogeneous Bianchi type-II, VIII & IX cosmological models with strange quark matter attached to string cloud in Brans and Dicke (Phys. Rev. C 71:054905, 1961) scalar tensor theory and general theory of gravitation. Some important features of the models, thus obtained, have been discussed. We noticed that these universes always expand isotropically and the presence of scalar field doesn’t affect the geometry of the space-time but changes the matter distribution.     

Letter: Constraint Propagation in (N + 1)-Dimensional Space-Time

Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for future numerical research of higher-dimensional space-time, we study the dimensional dependence of constraint propagation behavior. The N+1 Arnowitt-Deser-Misner evolution equation has matter terms which depend on N, but the constraints and constraint propagation equations remain the same. This indicates that there would be problems with accuracy and stability when we directly apply the N+1 ADM formulation to numerical simulations as we have experienced in four-dimensional cases. However, we also conclude that previous efforts in re-formulating the Einstein equations can be applied if they are based on constraint propagation analysis.     

What if? Exploring the multiverse through Euclidean wormholes

We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of third quantisation. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the current bounds on the energy scale of inflation and assuming that all the baby universes are nucleated with the same probability, we draw some conclusions about which universes are more likely to tunnel and therefore undergo a standard inflationary era.     

Bouncing scenario of general relativistic hydrodynamics in extended gravity

In this paper,we have framed bouncing cosmological model of the Universe in the presence of general relativistic hydrodynamics in an extended theory of gravity.The metric assumed here is the flat Friedmann–Robertson–Walker space–time and the stress energy tensor is of perfect fluid.Since general relativity(GR)has certain issues with late time cosmic speed up phenomena,here we have introduced an additional matter geometry coupling that described the extended gravity to GR.The dynamical parameters are derived and analyzed.The dynamical behavior of the equation of state parameter has been analyzed.We have observed that the bouncing behavior is mostly controlled by the coupling parameter.     

Is the universe expanding?

It is shown that spherically symmetric static general relativistic cosmological space-times can reproduce the same cosmological observations as the currently favored Friedmann-Robertson-Walker universes, if the usual assumptions are made about the local physical laws determining the behavior of matter, provided that the universe is inhomogeneous and our galaxy is situated close to one of its centers. Only (i) unverifiable a priori assumptions, (ii) detailed physical and astrophysical arguments, or (iii) observation of the time variation of cosmological quantities can lead us to conclude that the universe we live in is not such a static space-time.This essay was awarded the second prize for 1977 by the Gravity Research Foundation.     

Ordering chaos by random shortcuts

In this Letter, the effects of random shortcuts in an array of coupled nonlinear chaotic pendulums and their ability to control the dynamical behavior of the system are investigated. We show that random shortcuts can induce periodic synchronized spatiotemporal motions, even though all oscillators are chaotic when uncoupled. This process exhibits a nonmonotonic dependence on the density of shortcuts. Specifically, there is an optimal amount of random shortcuts, which can induce the most ordered motion characterized by the largest order parameter that is introduced to measure the spatiotemporal order. Our results imply that topological randomness can tame spatiotemporal chaos.     

Nearly everywhere flat spaces

We discuss some spacetimes, which are flat everywhere except for a thin shell of matter or a string of matter, in the framework of the Israel formalism. First we study spherically symmetric universes with a single sheet of matter. Then we show that the construction of a cosmic string as a limit of various thin shell distributions of matter leads to identical results.     

Kink dynamics in one-dimensional coupled map lattices

We examine the problem of the dynamics of interfaces in a one-dimensional space-time discrete dynamical system. Two different regimes are studied: the non-propagating and the propagating one. In the first case, after proving the existence of such solutions, we show how they can be described using Taylor expansions. The second situation deals with the assumption of a travelling wave to follow the kink propagation. Then a comparison with the corresponding continuous model is proposed. We find that these methods are useful in simple dynamical situations but their application to complex dynamical behaviour is not yet understood. (c) 1995 American Institute of Physics.     

Dissipative Cylindrical Collapse of Charged Anisotropic Fluid

We have studied the dynamics of a cylindrical column of anisotropic, charged fluid which is experiencing dissipation in the form of heat flow, free-streaming radiation, and shearing viscosity, undergoing gravitational collapse. We calculate the Einstein-Maxwell field equations and, using the Darmois junction conditions, match the interior non-static cylindrically symmetric space-time with the exterior anisotropic, charged, cylindrically symmetric space-time. The behavior of the density, pressure and luminosity of the collapsing matter has been analyzed. From the dynamical equations, the effect of charge and dissipative quantities over the cylindrical collapse are studied. Finally, we have derived the solutions for the collapsing matter which is valid during the later stages of collapse and have discussed the significance from a physical standpoint.     

The premature recollapse problem in closed inflationary universes

We discuss whether closed universe can avoid recollapsing before inflation ensues. We show that in general closed universe are not equivalent to recollapsing universes or positive curvature universes. Closed universes will not in general recollapse if the matter content violates the strong energy condition. This violation is also a necessary condition for inflation to occur. When the strong energy condition holds closed universes can only recollapse if they possess S³ or S²×S¹ spatial topology. Even when the topology is S³ and the strong energy condition holds it is not known whether anisotropic closed universes do all recollapse. We give examples to show that closed universes which begin in an extremely anisotropic state cannot recollapse until they are close to isotropy. This suggests that if the initial conditions prior to inflation are sufficiently anisotropic then the universe cannot recollapse until it has been isotropized by inflation. We also discuss the existence of inflation in isotropic cosmological models in R+R² lagrangian theories of gravity and extend a result of Whitt to show that such theories are conformally equivalent to general relativity plus a scalar field with an asymmetric potential.     

Brane world generated dynamically from string type IIB matrices

We have recently proposed a dynamical mechanism that may realize a flat four-dimensional space-time as a brane in type IIB superstring theory. A crucial role is played by the phase of the chiral fermion integral associated with the IKKT (Ishibashi-Kawai-Kitazawa-Tsuchiya) matrix theory, which is conjectured to be a nonperturbative definition of type IIB superstring theory. We demonstrate our mechanism by studying a simplified model, in which we find that a lower-dimensional brane indeed appears dynamically. We also comment on some implications of our mechanism on model building of the brane world.