Bianchi Type-I Space-Time with Variable Cosmological Constant

A spatially homogeneous and anisotropic Bianchi type-I perfect fluid model is considered with variable cosmological constant. Einstein’s field equations are solved by using a law of variation for mean Hubble’s parameter, which is related to average scale factor and that yields a constant value of deceleration parameter. An exact and singular Bianchi-I model is presented, where the cosmological constant remains positive and decreases with the cosmic time. It is found that the solutions are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the model is carried out.     

Cosmological models in general relativity

LRS Bianchi type-I space-time filled with perfect fluid is considered here with deceleration parameter as variable. The metric potentialsA andB are functions of x as well as t. Assuming B′/B = f (x), where prime denotes differentiation with respect to x, it was found thatA = (l′/l)B andB = lS(t), wherel = f (x) andS is the scale factor which is a function of t only. The value of Hubble’s constantH ₀ was found to be less than half for non-flat model and is equal to 1.3 for a flat model     

Conformally flat tilted Bianchi Type-V cosmological models in general relativity

We have investigated two conformally flat tilted Bianchi Type-V cosmological models in general relativity. To get a determinate solution, we have assumed a supplementary conditionA =B ⁿ between metric potentials wheren is a constant. The behaviour of the model forn = 2 is discussed in detail. Various physical and geometrical aspects of the models are also discussed.     

A new class of LRS Bianchi type-I cosmological models in Lyra geometry

LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe. The physical behaviour of the models is examined in vacuum and in the presence of perfect fluids.     

Cosmological models with constant deceleration parameter in Nordtvedt’s theory

Exact solutions of the field equations of Nordtvedt’s theory for spatially flat FRW models with constant deceleration parameter have been obtained. Singular solutions with (i) power-law (ii) exponential expansion have been studied in Nordtvedt’s theory where the coupling parameterω is a function of the scalar fieldφ.     

Bianchi Type-IX viscous fluid cosmological model in general relativity

Bianchi Type-IX viscous fluid cosmological model is investigated. To get a deterministic model, we have assumed the conditiona = b ^m(m is a constant) between metric potentials andη ∞θ whereη is the coefficient of shear viscosity andθ the scalar of expansion in the model. The coefficient of bulk viscosity (ς) is taken as constant. The physical and geometrical aspects of the model are also discussed.     

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.     

A higher-dimensional Bianchi type-I inflationary Universe in general relativity

A five-dimensional Bianchi type-I inflationary Universe is investigated in the presence of massless scalar field with a flat potential. To get an inflationary Universe, a flat region in which the potential V is constant is considered. Some physical and kinematical properties of the Universe are also discussed.     

LRS Bianchi type I models with anisotropic dark energy and constant deceleration parameter

Locally rotationally symmetric Bianchi type I cosmological models are examined in the presence of dynamically anisotropic dark energy and perfect fluid. We assume that the dark energy (DE) is minimally interacting, has dynamical energy density, anisotropic equation of state parameter (EoS). The conservation of the energy-momentum tensor of the DE is assumed to consist of two separately additive conserved parts. A special law is assumed for the deviation from isotropic EoS, which is consistent with the assumption on the conservation of the energy-momentum tensor of the DE. Exact solutions of Einstein’s field equations are obtained by assuming a special law of variation for the mean Hubble parameter, which yields a constant value of the deceleration parameter. Geometrical and kinematic properties of the models and the behaviour of the anisotropy of the dark energy have been carried out. The models give dynamically anisotropic expansion history for the universe that allows to fine tune the isotropization of the Bianchi metric, hence the CMB anisotropy.     

Cosmological models with constant deceleration parameter

Berman presented elsewhere a law of variation for Hubble's parameter that yields constant deceleration parameter models of the universe. By analyzing Einstein, Pryce-Hoyle and Brans-Dicke cosmologies, we derive here the necessary relations in each model, considering a perfect fluid.     

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.     

The graviton one-loop effective action in cosmological space-times with constant deceleration

We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gravitons and scalar field matter in a FLRW background with constant . After several field redefinitions, to remove the mixing between the gravitational and matter degrees of freedom, we can construct the one-loop correction to the Friedmann equations. Due to cosmological particle creation, the propagators needed in such a calculation are typically infrared divergent. In this paper we construct the graviton and matter propagators, making use of the recent construction of the infrared finite scalar propagators calculated on a compact spatial manifold in Janssen et al. (2008) [1]. The resulting correction to the Friedman equations is suppressed with respect to the tree level contribution by a factor of and shows no secular growth.     

Tilted Bianchi type I dust fluid cosmological model in general relativity

In this paper, we have investigated a tilted Bianchi type I cosmological model filled with dust of perfect fluid in general relativity. To get a determinate solution, we have assumed a condition A = B ⁿ between metric potentials. The physical and geometrical aspects of the model together with singularity in the model are also discussed.     

Bianchi Type V Cosmological Models with Constant Deceleration Parameter in General Relativity

We investigate Bianchi type V cosmological models with bulk viscous fluid source. Exact solutions of the Einstein field equations are presented via a suitable power law assumption for the Hubble parameter. We show that the corresponding solutions retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Some observational parameters for the models have also been discussed.     

Bianchi type-I bulk viscous fluid string dust magnetized cosmological model in general relativity

Bianchi Type-I magnetized bulk viscous fluid string dust cosmological model is investigated. To get a determinate model, we have assumed the conditions σ ∝θ andζθ = constant where σ is the shear,θ the expansion in the model andζ the coefficient of bulk viscosity. The behaviour of the model in the presence and absence of magnetic field together with physical and geometrical aspects of the model are also discussed.     

Anisotropic dark energy models with constant deceleration parameter

We consider a spatially homogeneous and totally anisotropic Bianchi-I space-time with perfect fluid (dark matter and standard visible matter) and anisotropic dark energy, which has dynamical energy density. The two sources are assumed to interact minimally and therefore their energy momentum tensors are conserved separately. Using suitable physical assumptions, the field equations are solved exactly. Various dark energy models are studied and it is found that quintessence model is suitable for describing the present evolution of the universe. The geometrical and kinematical features of the models and the behavior of the anisotropy of the dark energy, are examined in detail.     

Cosmological models with constant deceleration parameter in Brans-Dicke theory

A detailed study of cosmological models with constant deceleration parameterq is undertaken in the framework of Brans-Dicke theory. These models are divided into two categories: (i) singular models with expansion driven by big-bang impulse, (ii) non-singlar models with expansion driven by creation of matter particles. Prigogine's hypothesis of creation of matter out of gravitational energy is analysed and extended to BD cosmology. To accommodate the creation of new particles, the universe is regarded as an open thermodynamical system and the energy conservation equation is modified with the incorporation of a creation pressure termp _c in the energy-momentum tensor . The exact solutions of the field equations of BD theory with are obtained using the power law relation=KR , which leads to models with constantq. The behaviour of the solutions is investigated for different range of values ofa. The role played by the BD scalar field and creation of matter particles in the expansion of the universe is investigated. It is found that one particular model with constantq has exponential expansion.     

Bianchi type-V string cosmological models in general relativity

Bianchi type-V string cosmological models in general relativity are investigated. To get the exact solution of Einstein’s field equations, we have taken some scale transformations used by Camci et al [Astrophys. Space Sci. 275, 391 (2001)]. It is shown that Einstein’s field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. Some physical and geometrical aspects of the models are discussed.