General Properties of Cosmological Models with an Isotropic Singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a -law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.     

Some Anisotropic Homogeneous Cosmological Models in Self-creation Cosmology

The paper presents an exact solution of cylindrically symmetric cosmological models which are of Petrov type-I or Petov type-D in Barber’s second self-creation theory of gravitation. Some physical and geometrical properties of these models are also discussed.     

“Golden Oldie”: The Spatially Homogeneous Cosmological Models

Schücking's program of calculating all spatially homogeneous dust-filled spacetimes is presented.     

Power Asymptotes of Homogeneous Cosmological Models in Einstein's Theory of Gravitation

Completing the discussion of an earlier treatment (Borzeszkowski, Müller (1978)) homogeneous cosmological models of Bianchi-types II, III, IV, VI and the models of Kantowski-Sachs-type are investigated. All asymptotes of the metric which have a power like dependence on the synchronized time near the cosmological singularity are listed. We assume an ideal fluid as source with the flow velocity orthogonal to the slices of homogeneity, and an equation of state π = β? 0 ? β ? 1. We utilize the fact that certain Bianchi types can be obtained by a limiting process from other ones. Special anisotropic matter-dominated solutions have been found besides the well-known Kasner asymptote.     

Power Asymptotes of Homogeneous Cosmological Models in Einstein's Theory of Gravitation

For the Bianchi-types I, V, VII, VIII, and IX, the asymptotes of the metric, which show a power-like dependence on the synchronized time t near the cosmological singularity, are investigated. Comparing the influence of the terms which in Einstein's equations describe time-derivatives, spatial curvature, and matter, on the behaviour of the asymptotes, different assumptions and conjectures usually used in literature are discussed for the equations of state p = β? (0 ? β ? 1). For Bianchi-type-IX models both the outgoing power-asymptotes and the oscillatory phase for t → 0 are considered.     

Anisotropic Cosmological Models with Variable G and Decaying Vacuum Energy

We present Bianchi type-I cosmological models with a perfect fluid source and time-dependent gravitational and cosmological constants based on new exact solutions of Einstein’s equations. The perfect fluid is chosen to obey a barotropic equation of state. The models obtained represent a radiation dominated phase and a dust era. In some of the models the expansion changes from a decelerating phase to an accelerating one and these models asymptotically tend to the de Sitter universe. The paper is dedicated to late Prof. S.R. Roy, Ex-Head, Department of Mathematics, Banaras Hindu University, Varanasi, India.     

Cosmological Constant and Stability of the Cosmological Models

The importance of cosmological constant for the cosmological models is given. The variations of the cosmological model for parameters λ and k were discussed respectively. Near λ = 0, the cosmological model is unstable with the change of λ, and near λ = β = 0, the cosmological model is unstable with the change of k. So when we consider the stable cosmological model, we must consider the nonzero cosmological constant.     

Late Time Isotropy Viewed Through Bianchi Type I Cosmological Models with Vacuum Energy

We investigate Bianchi type I cosmological models for perfect fluid source with time-dependent cosmological term Λ. We explore the possibility of cosmological models assuming the expansion anisotropy (the ratio σ/θ of the shear scalar σ to the volume expansion θ) to be a function of average scale factor R. The resulting models begin with initial anisotropy and approach isotropy at late times. The models evolve with decelerating expansion and enters into accelerating phase for large values of t.     

Bianchi A Cosmological Models as the Simplest Dynamical Systems in R4

The behaviour of the vacuum non-tilted Bianchimodels of class A is studied in terms of dynamicalsystems theory. We introduce phase variables in whichthe Hamiltonian constraint is solved algebraically. It is shown that in these variables BianchiVIII and Bianchi IX models assume the form of afour-dimensional autonomous system with a polynomialvector field defined on the phase space, whereas Bianchi I and Bianchi II world models can be presentedas a one- and two-dimensional system, respectively. TheBianchi VI₀ and Bianchi VII₀ worldmodels are represented as a three-dimensional dynamicalsystem.     

Letter: A Study of Asymptotic Behavior of Homogeneous Cosmological Models with a Varying Cosmological Constant in Einstein-Cartan Theory: Cosmic No-Hair Theorem

We have investigated cosmic no-hair theorem with varying cosmological constant in homogeneous anisotropic Bianchi-models for Einstein-Cartan theory. We have taken the variation of to be as the square of the extrinsic curvature scalar and asymptotic behavior has been studied.     

Adiabatic Models of the Cosmological Radiative Era

We consider a generalization of the Lemaitre-Tolman-Bondi (LTB) solutions by keeping the LTB metric but replacing its dust matter source by an imperfect fluid with anisotropic pressure _ab . Assuming that total matter-energy density is the sum of a rest mass term, ^(m), plus a radiation ^(r) = 3p density where p is the isotropic pressure, Einstein's equations are fully integrated without having to place any previous assumption on the form of _ab . Three particular cases of interest are contained: the usual LTB dust solutions (the dust limit), a class of FLRW cosmologies (the homogeneous limit) and of the Vaydia solution (the vacuum limit). Initial conditions are provided in terms of suitable averages and contrast functions of the initial densities of ^(m), ^(r) and the 3-dimensional Ricci scalar along an arbitrary initial surface t = t _i . We consider the source of the models as an interactive radiation-matter mixture in local thermal equilibrium that must be consistent with causal Extended Irreversible Thermodynamics (hence _ab is shear viscosity). Assuming near equilibrium conditions associated with small initial density and curvature contrasts, the evolution of the models is qualitatively similar to that of adiabatic perturbations on a matter plus radiation FLRW background. We show that initial conditions exist that lead to thermodynamically consistent models, but only for the full transport equation of Extended Irreversible Thermodynamics. These interactive mixtures provide a reasonable approximation to a dissipative tight coupling characteristic of radiation-matter mixtures in the radiative pre-decoupling era.     

Cosmological string solutions in 4 dimensions from 5d black holes

We obtain cosmological four dimensional solutions of the low energy effective string theory by reducing a five dimensional black hole, and black hole-de Sitter solution of Einstein gravity down to four dimensions. The appearance of a cosmological constant in the five dimensional Einstein-Hilbert action produces special dilation potential in the four dimensional effective string action. Cosmological scenarios implemented by our solutions are discussed.     

Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation

We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the seale-covariant theory of gravitation proposed by Canuto et al. By applying the law of variation for Hubble＇s parameter, exact solutions of the field equations are obtained, which correspond to the model of the universe having a big-bang type singularity at the initial time t = 0. The cosmological model, evolving from the initial singularity, expands with power-law expansion and gives essentially an empty space for a large time. The physical and dynamical properties of the model are also discussed.     

A Comparison of the LVDP and ΛCDM Cosmological Models

We compare the cosmological kinematics obtained via our law of linearly varying deceleration parameter (LVDP) with the kinematics obtained in the ΛCDM model. We show that the LVDP model is almost indistinguishable from the ΛCDM model up to the near future of our universe as far as the current observations are concerned, though their predictions differ tremendously into the far future.