Viscous fluid cosmology with a cosmological constant

Exact solutions of the field equations for a Bianchi type-I space-time, filled with a viscous fluid and cosmological constant, are obtained. We utilize the constancy of deceleration parameter to get singular and non-singular solutions. We investigate a number of solutions with constant and time-varying cosmological constant together with a linear relation between shear viscosity and expansion scalar. Due to dissipative processes, the mean anisotropy and shear of the model tend to zero at a faster rate.     

Axially symmetric radiating cosmological model in a self-creation cosmology

An axially symmetric space time is considered in the presence of a perfect fluid source in Barbers (Gen. Relativ. Gravit. 14, 117, 1982) second self creation theory of gravitation. An exact radiating cosmological model is presented using a relation between the metric potentials. Some physical and kinematical properties of the model are also discussed.     

Newtonian cosmology with a varying gravitational constant

Newtonian cosmology is developed with the assumption that the gravitational constantG diminishes with time. The functional form adopted forG(t), a modification of a suggestion of Dirac, isG=A(k+t) ^–1, wheret is the age of the Universe and a small constantk is inserted to avoid a singularity in the two-body problem. IfR is the scale factor, normalized to unity at an epoch time , the differential equation is then . Here ₀ is the mean density at the epoch time. With the above form forG(t), the solution is reducible to quadratures.The scale factorR either increases indefinitely or has one and only one maximum. LetH ₀ be the present value of Hubble's constant /R and _0c the minimum density for a maximum ofR, i.e., for closure of the Universe. The conditions for a maximum lead to a boundary curve of _0c versusH ₀ and the numbers indicate strongly that thisG-variable Newtonian model corresponds to an open universe. An upward estimate of the age of the Universe from 10¹⁰ yr to five times such a value would still lead to the same conclusion.The present Newtonian cosmology appears to refute the statement, sometimes made, that the Dirac model forG necessarily leads to the conclusion that the age of the Universe is one-third the Hubble time. Appendix B treats this point, explaining that this incorrect conclusion arises from using all the assumptions in Dirac (1938). The present paper uses only Dirac's final result, viz,G(k+t)^–1, superposing it on the differential equation .     

On Newtonian cosmology with a varying gravitational constant

In a paper with the same title as this one, J. P. Vinti studies the effects a varying gravitational constant has upon Newtonian cosmology. In this paper an alternative approach for the analysis is given which obtains and improves upon some of Vinti's major results.Supported in part by a NSF Grant.     

Friedmann cosmology with a cosmological constant in the modified Brans-Dicke theory

Homogenous isotropic cosmologies in the presence of a cosmological constant A are studied in the modified Brans-Dicke theory. A class of exact solutions are obtained in Dicke's revised units for empty space as well as for the models filled with dust or radiation. Behaviour of these models near the singularity are discussed.     

String theory, cosmology and varying constants

In string theory the coupling `constants' appearing in the low-energy effective Lagrangian are determined by the vacuum expectation values of some (a priori) mass less scalar fields (dilaton, moduli). This naturally leads one to expect a correlated variation of all the coupling constants, and an associated violation of the equivalence principle. We review some string-inspired theoretical models which incorporate such a space time variation of coupling constants while remaining naturally compatible both with phenomenological constraints coming from geochemical data (Oklo; Rhenium decay) and with present equivalence principle tests. Barring a very unnatural fine-tuning of parameters, a variation of the fine-structure constant as large as that recently `observed' by Webb et al. in quasar absorption spectra appears to be incompatible with these phenomenological constraints. Independently of any model, it is emphasized that the best experimental probe of varying constants are high-precision tests of the universality of free fall, such as MICROSCOPE and STEP. This revised version was published online in July 2006 with corrections to the Cover Date.     

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).     

Brans-dicke cosmology and the cosmological constant: The spectrum of vacuum solutions

We study the Brans-Dicke vacuum field equations in the presence of a cosmological term A. Considering a Friedmann-Robertson-Walker metric with flat spatial sections (k=0), we provide a qualitative analysis of the solutions and investigate its asymptotic properties. The general solution of the field equations for arbitrary values ofw and A is obtained.Work supported by CNPq (Brazil).     

Five dimensional universe model with variable cosmological term Λ and a big bounce

We assume the four dimensional induced matter of the 5D Ricci flat bouncing cosmological solution contains a perfect fluid. The big bounce singularity of simple 5D cosmological model is studied with the cosmological term Λ=α ρ and Λ=β H ² where α and β are constants and ρ and H are respectively energy density and Hubble parameter. This big bounce singularity is found to be an event horizon at which the scale factor and mass density of the universe are finite, while the pressure is infinite.      

The Planck length as a cosmological constraint

Any attempt at unification of gravity with quantum physics inevitably leads to the Planck length, usually interpreted as defining the distance scale at which quantum corrections to general relativity are expected to become important. Here we arrive at a scalelength of the same magnitude from the cosmological requirement that gravitating vacuum or zero-point energy does not overdominate the dynamics of the Universe. Other cosmological considerations are again seen to imply such a constraining lower scalelength.     

Some consequences of a spatially varying cosmological constant in a spherically symmetric distribution of matter

This paper investigates the effects of the spatial variation of the cosmological constant λ on the spacetime geometry within and outside a massive object. It is seen that the variation of λ with the radial coordinate introduces non-trivial changes leading to spacetime closing on itself around a massive object. It may also be possible to generate interior solutions that lead to flat rotation curves of galaxies     

Photon-to-baryon ratio in the universe and time – dependent cosmological term

The photon-to-baryon ratio in the universe is much greater than unity (about10⁹); this fact is unexplained in the standard model of the universe; it can be explained by a photon creation process related to a time-dependent cosmological term. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bianchi type-I string cosmological model in the presence of a magnetic field: classical versus loop quantum cosmology approaches

A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmological string is considered. The first objective of this study is to investigate Einstein equations using a tractable assumption usually accepted in the literature. Quantum effects of the present cosmological model are examined in the framework of loop quantum cosmology. Finally we draw a parallel between the classical and quantum approaches.     

A search for a problem free cosmology

We explore features of a nonminimally coupled theory of scalar fields with an effective potential that supports non topological soliton solutions. It is suggested that a problem free cosmology results.     

The Sunyaev–Zel'dovich effect as a cosmological discriminator

We show how future measurements of the Sunyaev–Zel'dovich effect (SZE) can be used to constrain the cosmological parameters. We combine the SZ information expected from the Planck full-sky survey, N ( S ), where no redshift information is included, with the N ( z ) obtained from an optically identified SZ-selected survey covering less than 1 per cent of the sky. We demonstrate how with a small subsample (≈300 clusters) of the whole SZ catalogue observed optically it is possible to reduce the degeneracy among the cosmological parameters drastically. We have studied the requirements for performing the optical follow-up and we show the feasibility of such a project. Finally, we have compared the cluster expectations for Planck with those expected for Newton–XMM during their lifetimes. It is shown that, owing to its larger sky coverage, Planck will detect a factor of ∼5 times more clusters than Newton–XMM and also provide a larger redshift coverage.     

Cosmological models in generalized scalar-tensor theory with cosmological term and bulk viscosity

Exponential and power law solutions for homogeneous cosmological modelshave been discussed in a generalized scalar-tensor theory where both thecosmological term and coupling parameter are taken tobe functions of the scalar field , along with the bulk viscousstress of the cosmic fluid. Assuming simple relationships of the scalarfield with the cosmological term and the coupling parameter, all thesolutions are studied in Dicke's revised units. By use of a conformaltransformation, the solutions are also expressed in atomic units.     

Bianchi type V universe with bulk viscous matter and time varying gravitational and cosmological constants

We consider spatially homogeneous and anisotropic Bianchi type V space- time with a bulk viscous fluid source, and time varying gravitational constant G and cosmological term Λ. The coefficient of bulk viscosity ζ is assumed to be a simple linear function of the Hubble parameter H (i.e. ζ = ζ 0 + ζ 1 H , where ζ 0 and ζ 1 are constants). The Einstein field equations are solved explicitly by using a law of variation for the Hubble parameter, which yields a constant value of the deceleration parameter. Physical and kinematical parameters of the models are discussed. The models are found to be compatible with the results of astronomical observations.     

The cosmological constant as an eigenvalue of a Sturm-Liouville problem

It is observed that one of Einstein-Friedmann’s equations has formally the aspect of a Sturm-Liouville problem, and that the cosmological constant, Λ, plays thereby the role of spectral parameter (what hints to its connection with the Casimir effect). The subsequent formulation of appropriate boundary conditions leads to a set of admissible values for Λ, considered as eigenvalues of the corresponding linear operator. Simplest boundary conditions are assumed, namely that the eigenfunctions belong to L ² space, with the result that, when all energy conditions are satisfied, they yield a discrete spectrum for Λ>0 and a continuous one for Λ<0. A very interesting situation is seen to occur when the discrete spectrum contains only one point: then, there is the possibility to obtain appropriate cosmological conditions without invoking the anthropic principle. This possibility is shown to be realized in cyclic cosmological models, provided the potential of the matter field is similar to the potential of the scalar field. The dynamics of the universe in this case contains a sudden future singularity.     

Cluster contribution to the X-ray background as a cosmological probe

Extensive measurements of the X-ray background (XRB) yield a reasonably reliable characterization of its basic properties. Having resolved most of the cosmic XRB into discrete sources, the levels and spectral shapes of its main components can be used to probe both the source populations and also alternative cosmological and large-scale structure models. Recent observations of clusters seem to provide evidence that clusters formed earlier and are more abundant than predicted in the standard Λ cold dark matter (ΛCDM) model. This motivates interest in alternative models that predict enhanced power on cluster scales. We calculate predicted levels and spectra of the superposed emission from groups and clusters of galaxies in ΛCDM and in two viable alternative non-Gaussian  (χ²)  and early dark energy models. The predicted levels of the contribution of clusters to the XRB in the non-Gaussian models exceed the measured level at low energies and levels of the residual XRB in the 2–8 keV band; these particular models are essentially ruled out. Our work demonstrates the diagnostic value of the integrated X-ray emission from clusters, by considering also its dependences on different metallicities, gas and temperature profiles, Galactic absorption, merger scenarios and on a non-thermal pressure component. We also show that the XRB can be used for an upper limit for the concentration parameter value.