Bianchi Type-III String Cosmological Models

Bianchi type III space time is considered in the presence of cosmic strings in Einstein’s general theory of relativity. Exact cosmological models are presented with the help of relation C=B ⁿ between metric coefficients C and B. Some physical properties of the model in each cases are discussed.     

Expanding the Area of Gravitational Entropy

I describe how gravitational entropy is intimately connected with the concept of gravitational heat, expressed as the difference between the total and free energies of a given gravitational system. From this perspective one can compute these thermodyanmic quantities in settings that go considerably beyond Bekenstein's original insight that the area of a black hole event horizon can be identified with thermodynamic entropy. The settings include the outsides of cosmological horizons and spacetimes with NUT charge. However the interpretation of gravitational entropy in these broader contexts remains to be understood.     

Assisted Inflation in Bianchi VI0 Cosmologies

Exact models for Bianchi VI₀ spacetimes with multiple scalar fields with exponential potentials have been derived and analysed. It has been shown that these solutions, when they exist, attract neighbouring solutions in the two cases corresponding to interacting and non-interacting fields. Unlike the results obtained in a previous work dealing with the late-time inflationary behaviour of Bianchi VI₀ cosmologies, the knowledge of exact solutions has made possible to study in detail the occurrence of inflation before the asymptotic regime. As happened in preceding works, here as well inflation is more likely to happen with a higher number of non-interacting fields or a lower number of interacting scalar fields.     

Bianchi Type <Emphasis Type="Italic">VI</Emphasis><Subscript>0</Subscript> Magnetized Barotropic Bulk Viscous Fluid Massive String Universe in General Relativity

A model of a cloud formed by massive strings is studied in the context of the usual general relativity. This model is used as a source of Bianchi type VI ₀ massive with magnetic field and bulk viscosity. To get a determinate model, we assume that the expansion (θ) in the model is proportional to the shear (σ) and also the fluid obeys the barotropic equation of state. The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field and bulk viscosity is discussed.     

String Cosmological Models in Lyra Geometry

The Bianchi type-V cosmological solutions of massive strings have been investigated in the theory based on Lyra’s geometry in normal gauge, in the presence as well as absence of the magnetic field. The physical and kinematical behaviors of the models have also been discussed.     

String Cosmological Models with Magnetic Field

A new class of string cosmological models withand without magnetic field in the context of aspace-time with G₃ symmetry has beenpresented. In order to study the effects of magneticfield, the standard energy-momentum tensor is modified byincorporating additional term due to magnetic field. Thephysical and kinematical behaviours of the stringcosmological models have been discussed.     

Gravitational fields with space-times of Bianchi type IX

Spatially homogeneous space-times of Bianchi type IX are considered. A general scheme for the derivation of exact solutions of Einstein’s equations corresponding to perfect fluid plus pure radiation fields is outlined. Some simple rotating Bianchi type IX cosmological models are presented. The details of these solutions are also discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Higher Dimensional Cosmological Model With Gravitational and Cosmological "Constants"

In this paper we have considered a cosmological model representing a flat viscous universe with variable G and in the context of higher dimensional spacetime. It has been observed that in this model the particle horizon exists and the cosmological term varies as inverse square of time. The deceleration parameter and temperature are well within the observational limits. The model indicates matter and entropy generation in the early stages of the universe. Further, it is shown that our model generates all models obtained by Arbab and Singh et al. in four-dimensional space-time.     

Properties of Gravitational Waves in Cosmological General Relativity

The 5D Cosmological General Relativity theory developed by Carmeli reproduces all of the results that have been successfully tested for Einstein's 4D theory. However the Carmeli theory because of its fifth dimension, the velocity of the expanding universe, predicts something different for the propagation of gravity waves on cosmological distance scales. This analysis indicates that gravitational radiation may not propagate as an unattenuated wave where effects of the Hubble expansion are felt. In such cases the energy does not travel over very large length scales but is evanescent and dissipated into the surrounding space as heat.     

ESSAY: The Cosmological Constant Problem in Brane-Worlds and Gravitational Lorentz Violations

Brane worlds are theories with extra spatial dimensions in which ordinary matter is localized on a (3+1) dimensional submanifold. Such theories could have interesting consequences for particle physics and gravitational physics. In this essay we concentrate on the cosmological constant (CC) problem in the context of brane worlds. We show how extra-dimensional scenarios may violate Lorentz invariance in the gravity sector of the effective 4D theory, while particle physics remains unaffected. In such theories the usual no-go theorems for adjustment of the CC do not apply, and we indicate a possible explanation of the smallness of the CC. Lorentz violating effects would manifest themselves in gravitational waves travelling with a speed different from light, which can be searched for in gravitational wave experiments.     

Bound on the Q-Factor of a G-Constant Measuring Pendulum Device from Gravitational Stochastic Background

We discuss the possible effects of gravitational-wave stochastic background on the performance of a pendulum device such those used in precise measurements of the gravitational constant G. The variation Q of the quality factor Q of the pendulum induced by the stochastic background is evaluated, by using as numerical input the results obtained in gravitational antennas experiments. It is found |q|10^–10, completely negligible with respect to a typical value Q10⁵.     

Cosmological Models with Variable Cosmological and Gravitational “Constants” and Bulk Viscous Models

A viscous model with variable gravitational and cosmological constant has been considered. Several solutions are presented and some are shown to be equivalent to Berman, Kalligas et al. and Brans-Dicke solutions.     

Early Universe with Variable Gravitational and Cosmological Constants

Einstein field equations are considered in zero-curvature Robertson–Walker (R–W) cosmology with perfect fluid source and time-dependent gravitational and cosmological “constants.” Exact solutions of the field equations are obtained by using the ’gamma-law' equation of state p = (γ − 1)ρ in which γ varies continuously with cosmological time. The functional form of γ (R) is used to analyze a wide range of cosmological solutions at early universe for two phases in cosmic history: inflationary phase and Radiation-dominated phase. The corresponding physical interpretations of the cosmological solutions are also discussed.     

Bianchi Type I String Dust Magnetized Cosmological Models in Lyra Geometry

Bianchi type I string dust cosmological models in the presence and absence of magnetic field in the frame work of Lyra geometry are investigated. To get the deterministic model of the universe, we assume that the eigenvalue （σ^11） of shear tensor （σ^ii） is proportional to expansion （θ）. This leads to A = （BC）^n, where A, B, C are metric potentials and n is a constant. To discuss the results in terms of cosmic time t, we have considered n = 1. The physical and geometrical aspects＇ of the models and singularities in the models are also discussed.     

Bianchi Type-III Cosmic Strings and Domain Walls Cosmological Model in General Relativity

Bianchi type-III space time is considered in the presence of cosmic strings and thick domain walls source in the frame work of general relativity. Exact cosmological models using various cases of ρ=α λ and p=γ ρ are presented. It is observed that the behavior of these models (with cosmic strings and domain walls), based on their physical and kinematical properties, is found to be identical.     

Bianchi Type I String Dust Magnetized Cosmological Models in Lyra Geometry

Bianchi type I string dust cosmological models in the presence and absence of magnetic field in the frame work of Lyra geometry are investigated. To get the deterministic model of the universe, we assume that the eigenvalue (σ₁¹ ) of shear tensor (σ_i ^j ) is proportional to expansion (θ ). This leads to A =(BC)ⁿ, where A, B, C are metric potentials and n is a constant. To discuss the results in terms of cosmic time t, we have considered n = 1. The physical and geometrical aspects of the models and singularities in the models are also discussed.     

Gravitational Spin Entropy Production

Spin entropy production for particles with arbitrary spin moving in a curved spacetime is discussed. There is a Wigner rotation due to both the acceleration an the curvature, which causes an initial pure state to transform into a final mixed state. Depending on the spacetime characteristics, one may find paths on which there is no Wigner rotation and the state remains pure.     

Anisotropic Cosmological Models with Perfect Fluid and Dark Energy Reexamined

We consider a self consistent system of Bianchi type-I (BI) gravitational field and a binary mixture of perfect fluid and dark energy. The perfect fluid is taken to be the one obeying the usual equation of state, i.e., p = ξε, with ζ∉[0, 1] whereas, the dark energy is considered to be obeying a quintessence-like equation of state. The modification of the ordinary quintessence lies in the fact that its pressure becomes positive if the (dark) energy density exceeds some critical value. Exact solutions to the corresponding Einstein equations are obtained. The model in consideration gives rise to a Universe which is spatially finite. Depending on the choice of problem parameters the Universe is either close with a space-time singularity, or an open one which is oscillatory, regular and infinite in time. PACS numbers: 04.20.Ha, 03.65.Pm, 04.20.Jb     

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.     

Exact Bianchi Type-I Cosmological Models in a Scalar-Tensor Theory

In this paper, a spatially homogeneous and anisotropic Bianchi type-I space-time filled with perfect fluid is investigated within the framework of a scalar-tensor theory proposed by Saez and Ballester. Two different physically viable models of the universe are obtained by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. One of the models is found to generalize a model recently investigated by Reddy et al. (Astrophys. Space Sci. 306:171, 2006). The Einstein’s field equations are solved exactly and the solutions are found to be consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models is carried out.