Higher-dimensional Bianchi type I cosmologies

We present here some general Bianchi type I solutions in (9+1)-dimensional space-time in the following cases: (A) vacuum field with (i) non-vanishing, (ii) vanishing cosmological constant Λ, and (B) dust model. We also discuss briefly some physical features of these solutions.     

Bianchi type I string cosmologies

By making use of Letelier’s form of energy—momentum tensor for a cloud of stringdust we present some classes of solutions of general relativistic field equations which describe cosmological string-dust models in Bianchi type I space-time. Some of the classes of models obey Takabayashi’s equation of state whereas a class of models exhibits inflation in the initial stage. Two of the classes presented here have Kasner’s space-time as past asymptote     

Bianchi type I inflationary universe in general relativity

In this paper, we have investigated Bianchi type I inflationary universe in the presence of massless scalar field with a flat potential. To get an inflationary solution, we have considered a flat region in which potential V is constant. The inflationary scenario of the model is discussed in detail.     

Strings in some Bianchi type cosmologies

Some Bianchi type cosmological models-two in four and one in higher dimensions-are here studied in the context of cosmic strings. The physical implications of the models are briefly discussed. It is interesting to note that cosmic strings do not occur in Bianchi type V cosmology.     

Bianchi I in scalar and scalar-tensor cosmologies

We study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) (“quintessence”) with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.     

Bianchi type V perfect fluid cosmologies

Bianchi type V solutions of the Einstein equations are studied using the Hamiltonian approach. Explicit expressions depending on a single quadrature are given for the metric components in the general orthogonal perfect fluid case. It is shown that the quadrature can be evaluated in terms of elementary or elliptic integrals when the parameter in the equation of statep=(–1) takes the values 1, 10/9, 4/3, 14/9, 5/3, 2.     

Bianchi type I expanding universe in Weyl-invariant gravity with a quartic interaction term

We will focus on the effect of a Weyl-invariant model with a quadratic interaction term and a free scalar field \(\psi \). A set of analytic solutions will be obtained for this model. This model provides a dynamical alternative to the standard \(\Lambda \)CDM model. In particular, we will show that the quartic Weyl-invariant model prediction is consistent with the Hubble diagram observations.     

Two Bianchi type VIII spatially homogeneous cosmologies

We study two Bianchi type VIII analogues of Taub space and maximal analytic extensions of them. The first one has SL(2,R) as an isometry group, which acts transitively on spacelike hypersurfaces. The maximal extension has all of the pathological features of Taub-NUT space. The second one has the universal covering group of SL(2,R) as an isometry group. The maximal extension of the latter does not have these pathological properties and is geodesically complete.Work supported in part by NSF Grant MPS 74-16311 AO1     

Electromagnetic Bianchi cosmologies

All exact solutions of the Einstein-Maxwell equations of Bianchi type-I which are of physical importance have been found. The solutions represent non-locally rotationally symmetric universes with source-free electromagnetic fields and the matter content is a perfect fluid, with equation of state p=(γ?1)?(1?γ?2). Non-titled Bianchi type-II models are integrated for perfect fluid matter for all values of γ.     

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.     

Higher-dimensional Bianchi cosmologies

We present new higher-dimensional Bianchi cosmologies of class A. Our solutions given are of type Mⁿ = R × M³ × T^D where N = M³ are of types I, II, VI₀, VII⁰, VIII and IX. This spectrum of solutions includes the higher-dimensional versions of the Kasner solution and the mixmaster universe with stiff matter content.     

Scalar field fluctuations in the early universe

We compute the quantum fluctuations of a non-self-interacting but unstable scalar field of arbitrary mass during the period of inflation. Instead of treating the scalar field in a static De Sitter space, we begin with a scalar field in the Friedmann universe just before the start of inflation, and work out the dynamics of the growing quantum fluctuation of the field after it has entered into the inflationary epoch. We use the physically sensible method of Vilenkin to regularize the theory. We find that in all but two special cases the fluctuations produced are different from those in a static De Sitter space, and the effect of the finite width of the scalar field limits the growth of fluctuations.     

Some rotating,time-dependent Bianchi type VIII cosmologies with heat flow

A number of explicit, rotating and expanding cosmological solutions of the Einstein field equations are presented. They have homogeneous hypersurfaces of Bianchi type VIII, and they are locally rotationally symmetric. The source is a perfect fluid with heat flow. The thermodynamic properties of the models are discussed.     

Scalar field fluctuations in the expanding universe and the new inflationary universe scenario

The behaviour of the scalar fied fluctuations in the exponentially expanding universe and their role in the new inflationary universe scenario are investigated.     

Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter

This paper is a study of the effects of anisotropic matter sources on the qualitative evolution of spatially homogenous cosmologies of Bianchi type VIII. The analysis is based on a dynamical system approach and makes use of an anisotropic matter family developed by Calogero and Heinzle which generalises perfect fluids and provides a measure of deviation from isotropy. Thereby the role of perfect fluid solutions is put into a broader context. The results of this paper concern the past and future asymptotic dynamics of locally rotationally symmetric solutions of type VIII with anisotropic matter. It is shown that solutions whose matter source is sufficiently close to being isotropic exhibit the same qualitative dynamics as perfect fluid solutions. However a high degree of anisotropy of the matter model can cause dynamics to differ significantly from the vacuum and perfect fluid case.