Bianchi-type Models Research Articles

Isotropization of N-component orthogonal fluid within the framework of Einstein field equations

In this study, we build up a general formalism for tilted N-component fluid form to investigate the isotropization features of the Bianchi-type models excluding Bianchi-IX. We applied this formalism to Bianchi type I and V models analytically and numerically using the metric approach of Einstein field equations. It is found that only the stiff fluid for Bianchi I model does not isotropize, in the absence of cosmological constant. Other Bianchi type I and V models become isotropic regardless of the type of the fluid or how much component it has. The result does not change with the existence of a cosmological constant.

Anisotropic homogeneous string cosmology with two-loop corrections

The two-loop (order α′) β-function equations, which are equivalent to the equations of motion of α′-corrected string effective action, are considered for anisotropic homogeneous space–times. These equations are solved for all Bianchi-type models in two schemes of effective action, namely R2 and Gauss–Bonnet schemes with zero cosmological constant and then the metric, dilaton and B-field are found at α′ perturbative corrections.

Kantowski-Sachs and Bianchi type models with a general non-canonical scalar field

The paper deals with spatially homogeneous and anisotropic Kantowski-Sachs and Bianchi universes with a general non-canonical scalar field with the Lagrangian L = F(X) − Ω(ϕ), where $$X = \frac{1}{2}{\phi _i}{\phi ^i}$$ . We discuss a general non-canonical scalar field in three different cosmologies: (i) cosmology with a constant potential, Ω(ϕ) = Ω0 = const, (ii) cosmology with a constant equation-of-state parameter, i.e., γϕ = const, and (iii) cosmology with a constant speed of sound, i.e., c s 2 = const. For a constant potential, we have shown that the k-essence Lagrangian and the Lagrangian of the present model are equivalent. Dissipation of anisotropy, when the universe is filled with a general non-canonical scalar field, is investigated. The existence of an average bounce in Kantowski-Sachs and locally rotationally symmetric Bianchi-I and Bianchi-III models is discussed in detail.

Bounce conditions in Kantowski–Sachs and Bianchi cosmologies in modified gravity theories

Many cosmological scenarios envisage either a bounce of the universe at early times, or a collapse locally to form a black hole which re-expands into a new expanding universe region. Energy conditions preclude this phenomena for ordinary matter in general relativistic universe, but scalar or other types of fields can violate some of these conditions, and so can, possibly, provide conditions for a bouncing universe. In this paper, we have investigated the necessary conditions for a bounce in Kantowski–Sachs (KS) and Bianchi type models in some modified theories of gravity like Hoyle–Narlikar creation field theory, Lyra geometry, general class of scalar–tensor theories, Einstein's theory with variable cosmological term.

Time-dependent automorphism-inducing diffeomorphisms, open algebras and the generality of the Kantowski–Sachs vacuum geometry

Following the spirit of a previous work of ours, we investigate the group of those general coordinate transformations (GCTs) which preserve manifest spatial homogeneity. In contrast to the case of Bianchi type models, here we permit an isometry group of motions G4 = SO(3) ⊗ Tr, where Tr is the translations group, along the radial direction, while SO(3) acts multiply transitively on each hypersurface of simultaneity Σt. The basis 1-forms cannot be invariant under the action of the entire isometry group and hence produce an open Lie algebra. In order for these GCTs to exist and have a nontrivial, well-defined action, certain integrability conditions have to be satisfied; their solutions, exhibiting the maximum expected ‘gauge’ freedom, can be used to simplify the generic, spatially homogeneous, line element. In this way an alternative proof of the generality of the Kantowski–Sachs (KS) vacuum is given, while its most general, manifestly homogeneous, form is explicitly presented.

SCALE FACTOR DUALITY IN STRING BIANCHI COSMOLOGIES

We apply the scale factor duality transformations introduced in the context of the effective string theory to the anisotropic Bianchi-type models. We find dual models for all the Bianchi-types [except for types VIII and IX] and construct for each of them its explicit form starting from the exact original solution of the field equations. It is emphasized that the dual Bianchi class B models require the loss of the initial homogeneity symmetry of the dilatonic scalar field.

Anisotropic cosmological scaling solutions

We study spatially homogeneous models with a perfect fluid and a scalar field with an exponential potential and we show that in addition to the usual isotropic spatially flat scaling solutions there are anisotropic scaling solutions. We discuss the stability of these anisotropic scaling solutions within a particular class of Bianchi type models.

Supersymmetric action for Bianchi type models

The superfield action for Bianchi type models is formulated on the basis of local n = 2 supersymmetry. It is shown that the supersymmetric action for these models has the form of the localized version of n = 2 supersymmetric quantum mechanics. This local symmetry procedure provides a well defined scheme for including matter.

Exact quantum state for N=1 supergravity.

For N=1 supergravity in 3+1 dimensions we determine the graded algebra of the quantized Lorentz generators, supersymmetry generators, and diffeo-morphism and Hamiltonian generators and find that, at least formally, it closes in the chosen operator ordering. Following our recent conjecture and generalizing an ansatz for Bianchi-type models we proposed earlier we find an explicit exact quantum solution of all constraints in the metric representation.

Anisotropic spacetimes in homogeneous string cosmology

The dynamics of the early universe may have been profoundly influenced by spatial anisotropies. A search for such backgrounds in the context of string cosmology has uncovered the existence of an entire class of 4D spatially homogeneous but not necessarily isotropic spacetimes, analogous to the class of Bianchi-type models in general relativity. Leading-order solutions with vanishing cosmological constant but with non-vanishing dilaton and antisymmetric field are explicitly found for all types. This is a new class of solutions, whose isotropy limits reproduce all known and, further, all possible FRW-type of models in the string effective-action context considered. There is always an initial singularity and no inflation. Other features of the general solutions, including their behavior under abelian T duality are also discussed.

Anisotropic generalizations of the FRW string backgrounds

An entire class of non-isotropic generalizations of the FRW string backgrounds is presented, essentially supplying the string-cosmology counterpart of the diagonal Bianchi-type models in general relativity. Leading-order solutions with vanishing cosmological constant and time-depended axion/dilation scalars have been found for all types. They include as special cases all hitherto known solution within this class, while the limits of SO(3) isotropy supply all possible FRW backgrounds. There is always an initial singularity and no inflation. Other features of the solutions which can illuminate the impact of spatial anisotropies on the dynamics of the early universe, as well as their behaviour under abelian T-duality, are discussed.

Cosmic no-hair theorem in power-law inflation.

We prove a cosmic no-hair theorem for Bianchi models in power-law inflation. Provided that the potential of an inflaton $\ensuremath{\varphi}$ is $\mathrm{exp}(\ensuremath{-}{\ensuremath{\lambda}}_{\ensuremath{\kappa}\ensuremath{\varphi}})$ with $0\ensuremath{\le}\ensuremath{\lambda}<\sqrt{\frac{2}{3}}$, we find that the isotropic power-law solution is the unique attractor for any initially expanding Bianchi-type models except type IX. For Bianchi type IX, this conclusion is also true if the initial ratio of the vacuum energy to the maximum three-curvature is larger than one half.

Certain vacuum Bianchi-type models in a new relativistic theory of gravitation

The vacuum Bianchi type-I, III, V, VI0 and Kantowski-Sachs models have been obtained in a new scalar-tensor theory formulated by Lau and Prokhovnik (1986) under the assumption of a certain relationship between the cosmological term Λ and the scalar field ψ. The dynamical behaviour of these models have been studied.