Bianchi type I two-fluid cosmological models with a variable G and Λ

This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I space–time with a variable gravitational constant G and cosmological constant Λ. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. We find a variety of solutions in which the cosmological parameter varies inversely with time t. We also discuss in detail the behavior of associated fluid parameters and kinematical parameters. This paper pictures cosmic history when the radiation and matter content of the universe are in an interactive phase. Here, Ω is closing to 1 throughout the cosmic evolution.      

Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on Lyra Manifold

An exact Bianchi type-V perfect fluid cosmological model is obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra Manifold in case of β is a constant and it is shown that this cosmological model exists only in the case of Radiation Universe (ρ=3p) if β is a function of ‘t’ using negative constant deceleration parameter. Some physical and geometrical properties of these models are discussed.     

Generalized de Sitter solution in multi-dimensional cosmology with static internal spaces

A multi-dimensional cosmological model with space-time consisting of n(n ≥ 2) Einstein spaces M_i is investigated in the presence of a cosmological constant λ and a homogeneous minimally coupled free scalar field. A generalized de Sitter solution was found for λ > 0 and a Ricci-flat external space for the case of static internal spaces with fine tuning of parameters.     

LRS Bianchi type-II massive string cosmological model in General Relativity

The present study deals with locally rotationally symmetric (LRS) Bianchi type II cosmological model representing massive string. The energy-momentum tensor for such string as formulated by Letelier (Phys. Rev. D 28:2414, 1983) is used to construct massive string cosmological model for which we assume that the expansion (θ) in the model is proportional to the shear (σ). This condition leads to A=B ^m , where A and B are the metric coefficients and m is proportionality constant. For suitable choice of constant m, it is observed that in early stage of the evolution of the universe string dominates over the particle whereas the universe is dominated by massive string at the late time. Our model is in accelerating phase which is consistent to the recent observations of type Is supernovae. Some physical and geometric behavior of the model is also discussed.     

Accelerating universe with time variation of G and Λ

We study a gravitational model in which scale transformations play the key role in obtaining dynamical G and Λ. We take a non-scale invariant gravitational action with a cosmological constant and a gravitational coupling constant. Then, by a scale transformation, through a dilaton field, we obtain a new action containing cosmological and gravitational coupling terms which are dynamically dependent on the dilaton field with Higgs type potential. The vacuum expectation value of this dilaton field, through spontaneous symmetry breaking on the basis of anthropic principle, determines the time variations of G and Λ. The relevance of these time variations to the current acceleration of the universe, coincidence problem, Mach’s cosmological coincidence and those problems of standard cosmology addressed by inflationary models, are discussed. The current acceleration of the universe is shown to be a result of phase transition from radiation toward matter dominated eras. No real coincidence problem between matter and vacuum energy densities exists in this model and this apparent coincidence together with Mach’s cosmological coincidence are shown to be simple consequences of a new kind of scale factor dependence of the energy momentum density as ρ∼a ⁻⁴. This model also provides the possibility for a super fast expansion of the scale factor at very early universe by introducing exotic type matter like cosmic strings.     

Constraints on big bang models from structure formation

I review the constraints on standard big bang model arising from considerations related to structure formation. I will focus on two specific series of models though similar analysis can be performed for a wider class of models. The first one is a Ω = 1 model with non-zero cosmological constant and the second one is a Ω < 1 model with zero cosmological constant. The observational constraints which I shall discuss include the measurement of the Hubble’s constant, the ages of globular clusters, the abundance of rich clusters, the baryon content of galaxy clusters and the abundance of high redshift objects. These constraints limit the allowed range of the cosmological parameters and allow. for only a small region to survive. In particular, the aesthetically pleasing model with Ω = 1 and zero cosmological constant is ruled out by the observations. It seems necessary to fine-tune the theoretical parameters if they have to fall within the available space. This talk is based on the work in Baglaet al. (1996).     

Implications of a cosmological term coupled to matter

The possibility that the cosmological term is proportional toGU, whereG is the gravitational coupling andU is the mass density of the universe is proposed and discussed. WithG = constant, a cosmological model is obtained, which avoids the flatness and horizon problems and does not affect the well known predictions on the cosmic helium abundance which come from standard big bang cosmology. In such model, the deceleration parameter is a null constant, there is matter creation process throughout the universe at the rate 10^–47 g cm^–3 s^–1 and the cosmological term varies asH ² =t ^–2, whereH is the Hubble constant andt is the cosmic time.The possibility of a time-dependentG is then considered. The main consequence of this is that there is a mass creation process on the local scale; the rate of mass creation inside a body of massM is dM/dt =M H. In Section 6 it is suggested that the new matter might be in the form of neutrinos. This suggestion leads to an interesting consequence in celestial mechanics: the radius of a binary system should depend on time according to the nature of the components (the radius of a binary star should decrease, the radius of a planet-moon system should expand, and the orbital radius of a planet should stay constant).     

Bulk viscous LRS Bianchi-I Universe with variable G and decaying Λ

The present study deals with spatially homogeneous and totally anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with variable G and Λ in presence of imperfect fluid. To get the deterministic model of Universe, we assume that the expansion (θ) in the model is proportional to shear (σ). This condition leads to A=ℓB ⁿ , where A, B are metric potential. The cosmological constant Λ is found to be decreasing function of time and it approaches a small positive value at late time which is supported by recent Supernovae Ia (SN Ia) observations. Also it is evident that the distance modulus curve of derived model matches with observations perfectly.     

The inflationary Kantowski-Sachs cosmological model in general relativity

In this paper, we have investigated the inflationary Kantowski-Sachs cosmological model in the presence of mass less scalar field with a flat potential. To get an inflationary solution, we have considered a flat region of a constant potential V. Some physical and kinematical properties of the model are studied.     

Conformal analogs of the Jordan-Brans-Dicke theory. I.

Recent cosmological observations of large-scale structures (red shift of type Ia supernovae) confirm that the universe is currently expanding at an accelerating rate and its dominant component is dark energy. This has stimulated the development of the theory of gravity and led to many alternative variants, including tensor-scalar ones. This paper deals with the role of conformal transformations in the Jordan-Brans-Dicke theory. Variants of intrinsic, conformally coupled, and Einstein representations are examined. In the Einstein representation an exact analytic solution for the standard cosmological model is obtained. It is expressed in terms of the relative energy contributions of ordinary matter Ω _m , the scalar field Ω _CK , and a term Ω_Λ related to the cosmological constant Λ . Information on the evolution of the universe for the case with a minimally coupled scalar field is given in the form of graphs.     

Generalized Chaplygin gas model: cosmological consequences and statefinder diagnosis

The generalized Chaplygin gas (GCG) model in spatially flat universe is investigated. The cosmological consequences led by GCG model including the evolution of EoS parameter, deceleration parameter and dimensionless Hubble parameter are calculated. We show that the GCG model behaves as a general quintessence model. The GCG model can also represent the pressureless CDM model at the early time and cosmological constant model at the late time. The dependency of transition from decelerated expansion to accelerated expansion on the parameters of model is investigated. The statefinder parameters r and s in this model are derived and the evolutionary trajectories in s–r plane are plotted. Finally, based on current observational data, we plot the evolutionary trajectories in s–r and q–r planes for best fit values of the parameters of GCG model. It has been shown that although, there are similarities between GCG model and other forms of Chaplygin gas in statefinder plane, but the distance of this model from the ΛCDM fixed point in s–r diagram is shorter compare with standard Chaplygin gas model.     

Cosmological scalar fields that mimic the ΛCDM cosmological model

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard ΛCDM cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on z). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians; the cases of power-law kinetic term and power-law potential are considered. Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of Ω _m . To remove this degeneracy additional information is needed besides the data on large-scale geometry. The article is published in the original.     

Non-zero rest mass neutrinos and the cosmological constant

Recently it was pointed out that a non-zero cosmological constant can play a role in the formation of neutrino halos only in the case of neutrinos of very low rest mass (m _v <-0.1eV). However, phase-space considerations would requirem _v >50 eV if neutrinos dominate the missing mass in halos of large spiral galaxies and moreoverm _v >200 eV is implied in the case of dwarf spheroidals. These larger neutrino masses would be in conflict with observed constraints on the age of the Universe unless a cosmological constant is invoked.     

A class of cosmological solutions of Brans-Dicke theory with cosmological constant

We present a class of exact cosmological solutions of Brans-Dicke (B-D) equations with cosmological constant in flat Robertson-Walker metric. These solutions are based on the relation øR ⁿ= constant between the B-D field and the scale factor of the universe. This relation turns out to be consistent with the equation of statep =m for the cosmic matter, provided thatn andm are suitably related to each other. Several special cases and asymptotic solutions are derived and discussed.     

A note on variable-G cosmologies

An example of a cosmological model with variable gravitational couplingG and a time-dependent cosmological term , has recently been presented. It has been shown that there is no creation of matter and that the rest mass of particles stays constant in this model. In this paper we will generalize the field equations to the case where bothG and depend both on time and position. It is shown that even in this case there may be no creation.     

Emergent universe in Hor?ava gravity

Recently Hor̆ava has proposed a non-relativistic renormalisable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein’s gravity at large distances with a non-vanishing cosmological constant but with improved UV behaviour. In this paper, we have considered the Friedman-Lema?tre-Robertson-Walker cosmological model in Hor̆ava gravity and the emergent scenario for all values of the spatial curvature k (=0,±1) has been studied. As a result, there are constraints on the parameters involved.     

Non-expanding universe: a cosmological system of units

The product of two empirical constants, the dimensionless fine-structure constant (α) and the von Klitzing constant (R _k, an electrical resistance), turns out to be an exact dimensionless number. Then the accuracy and cosmological time variation (if any) of these two constants can be tied together. Also this product defines a natural unit of the electrical resistance, the inverse of a quantum of conductance. When the speed of light c is taken away from α, as has been shown elsewhere, the constancy of α implies the constancy of the ratio e ²/h (the inverse of the von Klitzing constant), e being the charge of the electron and h the Planck constant. This forces the charge of the electron e to be constant as long as the action h (an angular momentum) is a true constant too. From the constancy of the Rydberg constant the Compton wavelength, h/mc, is then a true constant and consequently there is no expansion at the quantum mechanical level. The momentum mc is also a true constant and then general relativity predicts that the universe is not expanding, as shown elsewhere. The time variation of the speed of light explains the observed Hubble red shift. And there is a mass-boom effect. From this a coherent cosmological system of constant units can be defined.     

Anisotropic cosmological models with bulk viscosity for variable <Emphasis Type="Italic">G</Emphasis> and Λ

In this paper we have considered axially symmetric Bianchi-I, Kantowski Sachs and Bianchi-III space-time models with bulk viscosity, where the gravitational constant G and the cosmological term Λ vary with time. In Einstein equations this variation in G and Λ are taken in such a way as to preserve the energy momentum tensor. Solutions are obtained with the cosmological term varying inversely with square of time.     

LRS Bianchi-I anisotropic cosmological model with dominance of dark energy

The present study deals with spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dominance of dark energy. To get the deterministic model of Universe, we assume that the shear scalar (σ) in the model is proportional to expansion scalar (θ). This condition leads to A=B ⁿ , where A, B are metric potential and n is positive constant. It has been found that the anisotropic distribution of dark energy leads to the present accelerated expansion of Universe. The physical behavior of the Universe has been discussed in detail.     

(An)Isotropic models in scalar and scalar-tensor cosmologies

We study how the constants G and Λ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (“quintessence”) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi V, VII₀ and IX, 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 arrive at the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.