Bianchi cosmologies with anisotropic matter: Locally rotationally symmetric models

The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following. (i) There exist matter models, compatible with the standard energy conditions, such that solutions of Bianchi type IX (closed cosmologies) need not necessarily recollapse; there is an open set of forever expanding solutions. (ii) Generic type IX solutions associated with a matter model like Vlasov matter exhibit oscillatory behavior toward the initial singularity. This behavior differs significantly from that of vacuum/perfect fluid cosmologies; hence “matter matters”. Finally, we indicate that our methods can probably be extended to treat a number of open problems—in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.     

Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein–Maxwell field equations for this gas becomes a dynamical system in a 4D phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3D sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H ₀ is negative. If H ₀ is positive the trajectories end up in a curvature singularity that can be, depending on initial conditions, isotropic or anisotropic. In particular, if the initial magnetic field intensity is sufficiently large the collapsing singularity will always be anisotropic and pointing in the same direction of the field.     

Low-energy electron impact cross-sections and rate constants of $$\hbox {NH}_2$$

In this paper, we have studied the anisotropic and homogeneous Bianchi type-VI ₀ Universe filled with dark matter and holographic dark energy components in the framework of general relativity and Lyra’s geometry. The Einstein’s field equations have been solved exactly by taking the expansion scalar (??) in the model is proportional to the shear scalar (σ). Some physical and kinematical properties of the models are also discussed.     

Isotropic Evolution of a JBD Anisotropic Bianchi Universe

I study the dynamical effects due to the Brans-Dicke scalar -field at the early stages of a supposedly anisotropic Universe expansion in the scalar-tensor cosmology of Jordan-Brans-Dicke. This is done considering the behaviour of the general solutions for the homogeneous model of Bianchi type VII in the vacuum case. I conclude that the Bianchi-VII₀ model shows an isotropic expansion and that its only physical solution is equivalent to a Friedman-Robertson-Walker spacetime whose evolution can, depending on the value of the JBD coupling constant, begin in a singularity and, after expanding (inflating, if > 0), shrink to another, or starting in a non-singular state, collapse to a singularity. I also conclude that the general Bianchi-VII _h (with h 0) models show strong curvature singularities producing a complete collapse of the homogeneity surfaces to 2D-manifolds, to 1D-manifolds or to single points. Our analysis depends crucially on the introduction of the so-called intrinsic time, , as the product of the JBD scalar field times a mean scale factor a ³ = a ₁ a ₂ a ₃, in which the finite-cosmological-time evolution of this universe unfolds into an infinite -range. These universes isotropize from an anisotropic initial state, thence I conclude that they are stable against anisotropic perturbations.     

Relativistie Cosmology With Quantum Corrections

Homogeneous isotropic, anisotropic, and inhomogeneous cosmological models are studied using Einstein's general relativity with quntum corrections in field theoretical approximation. In particular we discuss coherent scalar fields and curvature squared terms in the gravitational Lagrangian. The conformal equivalence of the field equations of fourth order to general relativity with a scalar field as source is an example of the geometrization of a matter field. The aemiclassical quantum eorrections of the scalar fields can avoid the initial cosmological singularity and they lead to an inflationary evolution stage as transient attrator. The review provides new points of view on questions like the probability of the inflationary stage and the question of mechanisms for multiple inflation.     

Bianchi type IX asymptotical behaviours with a massive scalar field: chaos strikes back

We use numerical integrations to study the asymptotical behaviour of a homogeneous but anisotropic Bianchi type IX model in General Relativity with a massive scalar field. As it is well known, for a Brans-Dicke theory, the asymptotical behaviour of the metric functions is ruled only by the Brans-Dicke coupling constant ₀ with respect to the value –3/2. In this paper we examine if such a condition still exists with a massive scalar field. We also show that, contrary to what occurs for a massless scalar field, the singularity oscillatory approach may exist in the presence of a massive scalar field having a positive energy density.     

Integrable Multicomponent Perfect Fluid Multidimensional Cosmology II: Scalar Fields

We consider anisotropic cosmological models with a universe of dimension 4 or higher, factorized into n 2 Ricci-flat spaces, containing an m-component perfect fluid of m non-interacting homogeneous minimally coupled scalar fields under special conditions. We describe the dynamics of the universe: It has a Kasner-like behaviour near the singularity and isotropizes during the expansion to infinity. Some of the models considered are integrable, and classical as well as quantum solutions are found. Some solutions produce inflation from nothing. There exist classical asymptotically anti-de Sitter wormholes, and quantum wormholes with discrete spectrum.     

Cosmological aspects of the gravitational interaction of a scalar field in the affine-metric theory of gravitation

The gravitational interaction of a scalar field, with allowance for the possible influence of the torsional and nonmetric nature of space-time, is investigated within the framework of the affine-metric theory of gravitation. The equations of the theory are derived from the variational principle. It is shown that in an affine-metric space, the combined Lagrangian of the gravitational and scalar fields with conformal coupling is reduced to the Lagrangian of the system of gravitational and axion fields in the general theory of relativity. All of the exact general solutions of the consistent system of equations of gravitational and scalar (massless) fields in the affine-metric space under consideration are obtained for all types of homogeneous Friedmann cosmological models, with the initial singularity being removed from some of them. Homogeneous, anisotropic cosmological models, for which all of the exact general solutions are also obtained, are investigated. Some of these models are nonsingular, and the effect of isotropization due to the torsional and nonmetric nature of space-time occurs for many of them. K. D. Ushinskii State Pedagogical University, Yaroslavl’. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 39–50, May, 1998.     

Cosmological constant in the Bianchi type-I-modified Brans-Dicke cosmology

In 1961, Brans and Dicke [1] provided an interesting alternative to general relativity based on Mach’s principle. To understand the reasons leading to their field equations, we first consider homogeneous and isotropic cosmological models in the Brans-Dicke theory. Accordingly we start with the Robertson-Walker line element and the energy tensor of a perfect fluid. The scalar field φ is now a function of the cosmic time only. Then we consider spatially homogeneous and anisotropic Bianchi type-I-cosmological solutions of modified Brans-Dicke theory containing barotropic fluid. These have been obtained by imposing a condition on the cosmological parameter Λ(φ). Again we try to focus the meaning of this cosmological term and to relate it to the time coordinate which gives us a collapse singularity or the initial singularity. On the other hand, our solution is a generalization of the solution found by Singh and Singh [2]. As far as we are aware, such solution has not been given earlier.     

Holographic Dark Energy Model with Quintessence in Bianchi Type-I Space-Time

In this paper, we have studied a homogeneous and anisotropic universe filled with matter and holographic dark energy components. Assuming deceleration parameter to be a constant, an exact solution to Einstein’s field equations in axially symmetric Bianchi type-I line element is obtained. A correspondence between the holographic dark energy models with the quintessence dark energy models is also established. Quintessence potential and the dynamics of the quintessence scalar field are reconstructed, which describe accelerated expansion of the universe.     

Holographic Dark Energy (DE) Cosmological Models with Quintessence in Bianchi Type-V Space Time

In this paper, author studied homogeneous and anisotropic Bianchi type-V universe filled with matter and holographic dark energy (DE) components. The exact solutions to the corresponding Einstein’s field equations are obtained for exponential and power-law volumetric expansion. The holographic dark energy (DE) EoS parameter behaves like constant, i.e. ω _Λ =?1, which is mathematically equivalent to cosmological constant (Λ) for exponential expansion of the model, whereas the holographic dark energy (DE) EoS parameter behaves like quintessence for power-law expansion of the model. A correspondence between the holographic dark energy (DE) models with the quintessence dark energy (DE) is also established. Quintessence potential and dynamics of the quintessence scalar field are reconstructed, which describe accelerated expansion of the universe. The statefinder diagnostic pair {r,s} is adopted to characterize different phases of the universe.     

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.     

Using EXCALC to study nondiagonal multidimensional spatially homogeneous cosmologies

The exterior calculus package EXCALC2, developed by Schrüfer, is used to implement Siklos' method on a computer. By an appropriate choice of the 1-form basis of spatially homogeneous cosmological models, making use of the time-dependent automorphisms of the Lie algebra, it is possible to obtain a compact form of Einstein's field equations for general models of this type. The explicit expression of the equations, obtained with the help of EXCALC2, is given here for two nondiagonal five-dimensional spatially homogeneous models, namely G₁ and G₈. These equations constitute an ideal tool for the study of the dynamics of these models: an oscillatory behavior has been found for model G₁, while model G₈ exhibits a monotonous kasnerian mode of approach to the initial singularity.     

Prandtl number effects in decaying homogeneous isotropic turbulence with a mean scalar gradient

Decaying homogeneous isotropic turbulence with an imposed mean scalar gradient is investigated numerically, thanks to a specific eddy-damped quasi-normal Markovian closure developed recently for passive scalar mixing in homogeneous anisotropic turbulence (BGC). The present modelling is compared successfully with recent direct numerical simulations and other models, for both very large and small Prandtl numbers. First, scalings for the cospectrum and scalar variance spectrum in the inertial range are recovered analytically and numerically. Then, at large Reynolds numbers, the decay and growth laws for the scalar variance and mixed velocity–scalar correlations, respectively, derived in BGC, are shown numerically to remain valid when the Prandtl number strongly departs from unity. Afterwards, the normalised correlation ρ_wθ is found to decrease in magnitude at a fixed Reynolds number when Pr either increases or decreases, in agreement with earlier predictions. Finally, the small scales return to isotropy of the scalar second-order moments is found to depend not only on the Reynolds number, but also on the Prandtl number.     

Asymptotic Regimes of Magnetic Bianchi Cosmologies

We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII₀, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII₀ cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII₀ cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.     

Cosmological Spacetimes Balanced by a Weyl Geometric Scale Covariant Scalar Field

A Weyl geometric approach to cosmology is explored, with a scalar field φ of (scale) weight −1 as crucial ingredient besides classical matter. Its relation to Jordan-Brans-Dicke theory is analyzed; overlap and differences are discussed. The energy-stress tensor of the basic state of the scalar field consists of a vacuum-like term Λg _{μ ν} with Λ depending on the Weylian scale connection and, indirectly, on matter density. For a particularly simple class of Weyl geometric models (called Einstein-Weyl universes) the energy-stress tensor of the φ-field can keep space-time geometries in equilibrium. A short glance at observational data, in particular supernovae Ia (Riess et al. in Astrophys. J. 659:98ff, 2007), shows encouraging empirical properties of these models.     

C-Field Cosmology in Higher Dimensions

Hoyle and Narlikar's C-field cosmology is extended in the framework of higher dimensional spacetime and a class of exact solutions is obtained. Adjusting the arbitrary constants of integration one can show that our model is amenable to the desirable property of dimensional reduction so that the universe ends up in an effective 4D one. Further with matter creation from the C-field the mass density steadies with time and the usual bigbang singularity is avoided. An alternative mechanism is also suggested which seems to provide matter creation in the 4D spacetime although total matter in the 5D world remains conserved. Quintessence phenomenon and energy conditions are also discussed and it is found that in line with the physical requirements our model admits a solution with a decelerating phase in the early era followed by an accelerated expansion later. Moreover, as the contribution from the C-field is made negligible a class of our solutions reduces to the previously known higher dimensional models in the framework of Einstein's theory.     

G-essence with Yukawa interactions

We study the g-essence model with Yukawa interactions between a scalar field φ and a Dirac field ψ. For the homogeneous, isotropic and flat Friedmann–Robertson–Walker universe filled with the such g-essence, the exact solution of the model is found. Moreover, we reconstruct the corresponding scalar and fermionic potentials which describe the coupled dynamics of the scalar and fermionic fields. It is shown that some particular g-essence models with Yukawa interactions correspond to the usual and generalized Chaplygin gas unified models of dark energy and dark matter. Also we present some scalar–fermionic Dirac–Born–Infeld models corresponding g-essence models with Yukawa interactions which again describe the unified dark energy–dark matter system.     

Scalar field cosmologies in a Bianchi type I universe

The dynamics of a homogeneous, anisotropic, spatially flat Bianchi type I universe filled with a scalar field is studied. Using the usual synchronous form of the line element, general exact solutions for the Einstein field equations are obtained in the case of the exponential-potential scalar field (V=Λexp(k?)) and in the case of the Barrow-Saich potential ( $V \sim \dot \varphi ^2 $ ). Conditions under which inflation can occur are discussed and the late-time behaviour of the models is also considered.     

Motion by Mean Curvature from the Ginzburg-Landau Interface Model

We consider the scalar field φ _t with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy . The potential V is even and strictly convex. We prove that under a suitable large scale limit the φ _t -field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure for the -field. Received: 1 February 1996 / Accepted: 2 July 1996