arXiv subjects

John D. Barrow

Publications and source records attributed to John D. Barrow.

At least 127 records · Page 7Linked to original sources

arXiv2007

The Ups and Downs of Cyclic Universes

We investigate homogeneous and isotropic oscillating cosmologies with multiple fluid components. Transfer of energy between these fluids is included in order to model the effects of non-equilibrium behavior on closed universes. We find exact solutions which display a range of new behaviors for the expansion scale factor. Detailed examples are studied for the exchange of energy from dust or scalar field into radiation. We show that, contrary to expectation, it is unlikely that such models can offer a physically viable solution to the flatness problem.

gr-qc↗

arXiv2006

On the evolution of universes in quadratic theories of gravity

We use a dynamical systems approach to investigate Bianchi type I and II universes in quadratic theories of gravity. Due to the complicated nature of the equations of motion we focus on the stability of exact solutions and find that there exists an isotropic FRW universe acting as a past attractor. This may indicate that there is an isotropisation mechanism at early times for these kind of theories. We also discuss the Kasner universes, elucidate the associated centre manifold structure, and show that there exists a set of non-zero measure which has the Kasner solutions as a past attractor. Regarding the late-time behaviour, the stability shows a dependence of the parameters of the theory. We give the conditions under which the de Sitter solution is stable and also show that for certain values of the parameters there is a possible late-time behaviour with phantom-like behaviour. New types of anisotropic inflationary behaviour are found which do not have counterparts in general relativity.

gr-qc↗

arXiv2006

The Dominant Balance at Cosmological Singularities

We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general relativity.

gr-qc↗

arXiv2006

Observable Effects of Scalar Fields and Varying Constants

We show by using the method of matched asymptotic expansions that a sufficient condition can be derived which determines when a local experiment will detect the cosmological variation of a scalar field which is driving the spacetime variation of a supposed constant of Nature. We extend our earlier analyses of this problem by including the possibility that the local region is undergoing collapse inside a virialised structure, like a galaxy or galaxy cluster. We show by direct calculation that the sufficient condition is met to high precision in our own local region and we can therefore legitimately use local observations to place constraints upon the variation of "constants" of Nature on cosmological scales.

gr-qc↗

arXiv2006

Cosmology in three dimensions: steps towards the general solution

We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows for a mathematically compact and physically transparent description of the 3-dimensional spacetimes. Using this information we review the features of homogeneous and isotropic 3-d cosmologies, provide a number of new solutions and study gauge invariant perturbations around them. The first-order formalism is then used to provide a detailed study of the most general 3-d spacetimes containing perfect-fluid matter. Assuming the material content to be dust with comoving spatial 2-velocities, we find the general solution of the Einstein equations with non-zero (and zero) cosmological constant and generalise known solutions of Kriele and the 3-d counterparts of the Szekeres solutions. In the case of a non-comoving dust fluid we find the general solution in the case of one non-zero fluid velocity component. We consider the asymptotic behaviour of the families of 3-d cosmologies with rotation and shear and analyse their singular structure. We also provide the general solution for cosmologies with one spacelike Killing vector, find solutions for cosmologies containing scalar fields and identify all the PP-wave 2+1 spacetimes.

gr-qc↗

arXiv2006

Cosmologies with Energy Exchange

We provide a simple mathematical description of the exchange of energy between two fluids in an expanding Friedmann universe with zero spatial curvature. The evolution can be reduced to a single non-linear differential equation which we solve in physically relevant cases and provide an analysis of all the possible evolutions. Particular power-law solutions exist for the expansion scale factor and are attractors at late times under particular conditions. We show how a number of problems studied in the literature, such as cosmological vacuum energy decay, particle annihilation, and the evolution of a population of evaporating black holes, correspond to simple particular cases of our model. In all cases we can determine the effects of the energy transfer on the expansion scale factor. We also consider the situation in the presence of anti-decaying fluids and so called phantom fluids which violate the dominant energy conditions.

gr-qc↗

arXiv2006

Decaying Gravity

We consider the possibility of energy being exchanged between the scalar and matter fields in scalar-tensor theories of gravity. Such an exchange provides a new mechanism which can drive variations in the gravitational 'constant' G. We find exact solutions for the evolution of spatially flat Friedman-Roberston-Walker cosmologies in this scenario and discuss their behaviour at both early and late times. We also consider the physical consequences and observational constraints on these models.

gr-qc↗

arXiv2006

The Existence of Godel, Einstein and de Sitter Universes

We determine the general conditions for the existence of Godel, Einstein static, and de Sitter universes in gravity theories derived from a Lagrangian that is an arbitrary function of the scalar curvature and Ricci and Riemann curvature invariants. Explicit expressions for the solutions are found in terms of the parameters defining the Lagrangian. We also determine the conditions on the Lagrangian of the theory under which time-travel is allowed in the Godel universes.

gr-qc↗

arXiv2006

Anisotropically Inflating Universes

We show that in theories of gravity that add quadratic curvature invariants to the Einstein-Hilbert action there exist expanding vacuum cosmologies with positive cosmological constant which do not approach the de Sitter universe. Exact solutions are found which inflate anisotropically. This behaviour is driven by the Ricci curvature invariant and has no counterpart in the general relativistic limit. These examples show that the cosmic no-hair theorem does not hold in these higher-order extensions of general relativity and raises new questions about the ubiquity of inflation in the very early universe and the thermodynamics of gravitational fields.

gr-qc↗

arXiv2006

Further Exact Cosmological Solutions to Higher-Order Gravity Theories

We investigate the effect of deviations from general relativity on approach to the initial singularity by finding exact cosmological solutions to a wide class of fourth-order gravity theories. We present new anisotropic vacuum solutions of modified Kasner type and demonstrate the extent to which they are valid in the presence of non-comoving perfect-fluid matter fields. The infinite series of Mixmaster oscillations seen in general relativity will not occur in these solutions, except in unphysical cases.

gr-qc↗

arXiv2006

The Local Effects of Cosmological Variations in Physical 'Constants' and Scalar Fields I. Spherically Symmetric Spacetimes

We apply the method of matched asymptotic expansions to analyse whether cosmological variations in physical `constants' and scalar fields are detectable, locally, on the surface of local gravitationally bound systems such as planets and stars, or inside virialised systems like galaxies and clusters. We assume spherical symmetry and derive a sufficient condition for the local time variation of the scalar fields that drive varying constants to track the cosmological one. We calculate a number of specific examples in detail by matching the Schwarzschild spacetime to spherically symmetric inhomogeneous Tolman-Bondi metrics in an intermediate region by rigorously construction matched asymptotic expansions on cosmological and local astronomical scales which overlap in an intermediate domain. We conclude that, independent of the details of the scalar-field theory describing the varying `constant', the condition for cosmological variations to be measured locally is almost always satisfied in physically realistic situations. The proof of this statement provides a rigorous justification for using terrestrial experiments and solar system observations to constrain or detect any cosmological time variations in the traditional `constants' of Nature.

gr-qc↗

arXiv2006

The Local Effects of Cosmological Variations in Physical 'Constants' and Scalar Fields II. Quasi-Spherical Spacetimes

We investigate the conditions under which cosmological variations in physical `constants' and scalar fields are detectable on the surface of local gravitationally-bound systems, such as planets, in non-spherically symmetric background spacetimes. The method of matched asymptotic expansions is used to deal with the large range of length scales that appear in the problem. We derive a sufficient condition for the local time variation of the scalar fields driving variations in 'constants' to track their large-scale cosmological variation and show that this is consistent with our earlier conjecture derived from the spherically symmetric problem. We perform our analysis with spacetime backgrounds that are of Szekeres-Szafron type. They are approximately Schwarzschild in some locality and free of gravitational waves everywhere. At large distances, we assume that the spacetime matches smoothly onto a Friedmann background universe. We conclude that, independent of the details of the scalar-field theory describing the varying `constant', the condition for its cosmological variations to be measured locally is almost always satisfied in physically realistic situations. The very small differences expected to be observed between different scales are quantified. This strengthens the proof given in our previous paper that local experiments see global variations by dropping the requirement of exact spherical symmetry. It provides a rigorous justification for using terrestrial experiments and solar system observations to constraint or detect any cosmological time variations in the traditional `constants' of Nature in the case where non-spherical inhomogeneities exist.

gr-qc↗

arXiv2005

Local Experiments See Cosmologically Varying Constants

We describe a rigorous construction, using matched asymptotic expansions, which establishes under very general conditions that local terrestrial and solar-system experiments will measure the effects of varying `constants' of Nature occurring on cosmological scales to computable precision. In particular, `constants' driven by scalar fields will still be found to evolve in time when observed within virialised structures like clusters, galaxies, and planetary systems. This provides a justification for combining cosmological and terrestrial constraints on the possible time variation of many assumed `constants' of Nature, including the fine structure constant and Newton's gravitation constant.

gr-qc↗

arXiv2005

The Power of General Relativity

We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to $R^{1+δ}$. This scale-free extension reduces to general relativity when $δ\to 0$. In order to constrain generalisations of general relativity of this power class we analyse the behaviour of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires $δ>0$ or $δ<-1/4$. The stable attractors of the evolution are found. By considering the synthesis of light elements (helium-4, deuterium and lithium-7) we obtain the bound $-0.017<δ<0.0012.$ We evaluate the effect on the power spectrum of clustering via the shift in the epoch of matter-radiation equality. The horizon size at matter--radiation equality will be shifted by $\sim 1%$ for a value of $δ\sim 0.0005.$ We study the stable extensions of the Schwarzschild solution in these theories and calculate the timelike and null geodesics. No significant bounds arise from null geodesic effects but the perihelion precession observations lead to the strong bound $δ=2.7\pm 4.5\times 10^{-19}$ assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound $0\leq δ<7.2\times 10^{-19}$ on theories of this type.

gr-qc↗

arXiv2005

Varying Constants

We review properties of theories for the variation of the gravitation and fine structure 'constants'. We highlight some general features of the cosmological models that exist in these theories with reference to recent quasar data that are consistent with time-variation in the fine structure 'constant' since a redshift of 3.5. The behaviour of a simple class of varying-alpha cosmologies is outlined in the light of all the observational constraints.

astro-ph↗

arXiv2005

Cosmological Co-evolution of Yang-Mills Fields and Perfect Fluids

We study the co-evolution of Yang-Mills fields and perfect fluids in Bianchi type I universes. We investigate numerically the evolution of the universe and the Yang-Mills fields during the radiation and dust eras of a universe that is almost isotropic. The Yang-Mills field undergoes small amplitude chaotic oscillations, which are also displayed by the expansion scale factors of the universe. The results of the numerical simulations are interpreted analytically and compared with past studies of the cosmological evolution of magnetic fields in radiation and dust universes. We find that, whereas magnetic universes are strongly constrained by the microwave background anisotropy, Yang-Mills universes are principally constrained by primordial nucleosynthesis and the bound is comparatively weak, and Omega_YM < 0.105 Omega_rad.

gr-qc↗

arXiv2005

Exact cosmological solutions of scale-invariant gravity theories

We have found new anisotropic vacuum solutions for the scale-invariant gravity theories which generalise Einstein's general relativity to a theory derived from the Lagrangian $R^{1+δ}$. These solutions are expanding universes of Kasner form with an initial spacetime singularity at $t=0 $ and exist for $-1/2<δ<1/4$ but possess different Kasner index relations to the classic Kasner solution of general relativity to which they reduce when $δ=0$. These solutions are unperturbed by the introduction of non-comoving perfect-fluid matter motions if $p<ρ$ on approach to the singularity and should not exhibit an infinite sequence of chaotic Mixmaster oscillations when $δ>0$.

gr-qc↗

arXiv2005

Cosmological Bounds on Spatial Variations of Physical Constants

We derive strong observational limits on any possible large-scale spatial variation in the values of physical 'constants' whose space-time evolution is driven by a scalar field. The limits are imposed by the isotropy of the microwave background on large angular scales in theories which describe space and time variations in the fine structure constant, the electron-proton mass ratio, and the Newtonian gravitational constant, G. Large-scale spatial fluctuations in the fine structure constant are bounded by 2x10^-9 and 1.2x10^-8 in the BSBM and VSL theories respectively, fluctuations in the electron-proton mass ratio by 9x10^-5 in the BM theory and fluctuations in G by 3.6x10^-10 in Brans-Dicke theory. These derived bounds are significantly stronger than any obtainable by direct observations of astrophysical objects at the present time.

astro-ph↗