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A. A. Coley

Publications and source records attributed to A. A. Coley.

At least 73 records · Page 4Linked to original sources
arXiv2002

Bianchi IX Brane-world Cosmologies

We shall investigate the asymptotic properties of the Bianchi type IX cosmological model in the Brane-world scenario. The matter content is assumed to be a combination of a perfect fluid and a minimimally coupled scalar field that is restricted to the Brane. A detailed qualitative analysis of the Bianchi type IX braneworld containing a scalar field having an exponential potential is undertaken. It is found that the Brane-Robertson Walker solution is a local source for the expanding Bianchi IX models, and if $k^2<2$ the expanding Bianchi IX models asymptote to the power-law inflationary solution. The only other local sink is the contracting Brane-Robertson Walker solution. An analysis of the Bianchi IX models with a scalar field with a general potential is discussed, and it is shown that in the case of expanding models, for physical scalar field potentials close to the initial singularity, the scalar field is effectively massless, and the solution is approximated by the Brane-Robertson Walker model.

gr-qc↗
arXiv2002

A Class of Exact Classical Solutions to String Theory

We show that the recently obtained class of spacetimes for which all of the scalar curvature invariants vanish (which can be regarded as generalizations of pp-wave spacetimes) are exact solutions in string theory to all perturbative orders in the string tension scale. As a result the spectrum of the theory can be explicitly obtained, and these spacetimes are expected to provide some hints for the study of superstrings on more general backgrounds. Since these Lorentzian spacetimes suffer no quantum corrections to all loop orders they may also offer insights into quantum gravity.

hep-th↗
arXiv2002

On Scaling Solutions with a Dissipative Fluid

We study the asymptotic behaviour of scaling solutions with a dissipative fluid and we show that, contrary to recent claims, the existence of stable accelerating attractor solution which solves the `energy' coincidence problem depends crucially on the chosen equations of state for the thermodynamical variables. We discuss two types of equations of state, one which contradicts this claim, and one which supports it.

gr-qc↗
arXiv2001

Qualitative Properties of Magnetic Fields in Scalar Field Cosmology

We study the qualitative properties of the class of spatially homogeneous Bianchi VI_o cosmological models containing a perfect fluid with a linear equation of state, a scalar field with an exponential potential and a uniform cosmic magnetic field, using dynamical systems techniques. We find that all models evolve away from an expanding massless scalar field model in which the matter and the magnetic field are negligible dynamically. We also find that for a particular range of parameter values the models evolve towards the usual power-law inflationary model (with no magnetic field) and, furthermore, we conclude that inflation is not fundamentally affected by the presence of a uniform primordial magnetic field. We investigate the physical properties of the Bianchi I magnetic field models in some detail.

astro-ph↗
arXiv2001

Magnetic Fields and the Cosmic Microwave Background

Observations of the high degree of isotropy of the cosmic microwave background are commonly believed to indicate that the Universe is `almost' Friedmann-Lemaitre-Robertson-Walker (at least since the time of last scattering). Theoretical support for this belief comes from the so-called Ehlers-Geren-Sachs Theorem. We show that a generalization of this theorem rules out any strong magnetic fields in the Universe. Our theoretical result is model-independent and includes the case of inhomogeneous magnetic fields, complementing previous results. We thus prove that cosmic microwave background observations severely constrain all types of primordial and protogalactic magnetic fields in the universe.

astro-ph↗
arXiv2001

The Cosmic Microwave Background and Scalar-Tensor Theories of Gravity

We show that if all observers see an isotropic cosmic microwave background in an expanding geodesic perfect fluid spacetime within a scalar-tensor theory of gravity, then that spacetime must be isotropic and spatially homogeneous. This result generalizes the Ehlers-Geren-Sachs Theorem of General Relativity, and serves to underpin the important result that any evolving cosmological model in a scalar-tensor theory that is compatible with observations must be almost Friedmann-Lemaitre-Robertson-Walker.

gr-qc↗
arXiv2000

The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models

The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the use of the physically interesting quantities arising in the comoving approach. We focus on three types of models. First, we consider models that are natural inhomogeneous generalizations of the Friedmann Universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the energy density at later times. Second, we consider so-called quasi-static models. This class includes models that undergo self-similar gravitational collapse and is important for studying the formation of naked singularities. If naked singularities do form, they have profound implications for the predictability of general relativity as a theory. Third, we consider a new class of asymptotically Minkowski self-similar spacetimes, emphasizing that some of them are associated with the self-similar solutions associated with the critical behaviour observed in recent gravitational collapse calculations.

gr-qc↗
arXiv2000

An asymptotic analysis of spherically symmetric perfect fluid self-similar solutions

The asymptotic properties of self-similar spherically symmetric perfect fluid solutions with equation of state p=alpha mu (-1 alpha >-1 or asymptotically static for 1>alpha >0. Others are associated with an approximate power-law solution, in which case they are asymptotically quasi-static for 1>alpha >0 or asymptotically Minkowski for 1>alpha >1/5. We also show that there are solutions whose asymptotic behaviour is associated with finite values of z and which depend upon powers of ln z. These correspond either to a second family of asymptotically Minkowski solutions for 1>alpha>1/5 or to solutions that are asymptotically Kasner for 1>alpha>-1/3. There are some other asymptotic power-law solutions associated with negative alpha, but the physical significance of these is unclear. The asymptotic form of the solutions is given in all cases, together with the number of associated parameters.

gr-qc↗
arXiv2000

Space-times admitting a three-dimensional conformal group

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dimensional conformal Lie group and the nature of their corresponding orbits (that are assumed to be non-null). Each metric is then explicitly displayed in coordinates adapted to the symmetry vectors. Attention is then restricted to the diagonal case, and exact perfect fluid solutions are obtained in both the cases in which the fluid four-velocity is tangential or orthogonal to the conformal orbits, as well as in the more general "tilting" case.

gr-qc↗
arXiv2000

The Dynamics of Multi-Scalar Field Cosmological Models and Assisted Inflation

We investigate the dynamical properties of a class of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials. We show that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions asymptotically the curvature is not dynamically negligible). Consequently, we find that in general all of the scalar fields in multi-field models with exponential potentials are non-negligible in late-time behaviour, contrary to what is commonly believed. The early-time and intermediate behaviour of the models is also studied. In particular, n-scalar field models are investigated and the structure of the saddle equilibrium points corresponding to inflationary m-field scaling solutions and non-inflationary m-field matter scaling solutions are also studied (where m<n), leading to interesting transient dynamical behaviour with new physical scenarios of potential importance.

gr-qc↗
arXiv1999

Critical phenomena and a new class of self-similar spherically symmetric perfect-fluid solutions

We consider the self-similar solutions associated with the critical behavior observed in the gravitational collapse of spherically symmetric perfect fluids with equation of state $p=αμ$. We identify for the first time the global nature of these solutions and show that it is sensitive to the value of $α$. In particular, for $α>0.28$, we show that the critical solution is associated with a new class of asymptotically Minkowski self-similar spacetimes. We discuss some of the implications of this for critical phenomena.

gr-qc↗
arXiv1999

Dynamical Systems in Cosmology

Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary differential equations. We begin with a brief review of dynamical systems theory. We then discuss cosmological models as dynamical systems and point out the important role of self-similar models. We review the asymptotic properties of spatially homogeneous perfect fluid models in general relativity. We then discuss some results concerning scalar field models with an exponential potential (both with and without barotropic matter). Finally, we discuss some isotropic cosmological models derived from the string effective action.

gr-qc↗
arXiv1999

Qualitative properties of scalar-tensor theories of Gravity

The qualitative properties of spatially homogeneous stiff perfect fluid and minimally coupled massless scalar field models within general relativity are discussed. Consequently, by exploiting the formal equivalence under conformal transformations and field redefinitions of certain classes of theories of gravity, the asymptotic properties of spatially homogeneous models in a class of scalar-tensor theories of gravity that includes the Brans-Dicke theory can be determined. For example, exact solutions are presented, which are analogues of the general relativistic Jacobs stiff perfect fluid solutions and vacuum plane wave solutions, which act as past and future attractors in the class of spatially homogeneous models in Brans-Dicke theory.

astro-ph↗
arXiv1999

Scalar Field Cosmologies with Barotropic Matter: Models of Bianchi class B

We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter content is composed of two non-interacting components; the first component is described by a barotropic fluid having a gamma-law equation of state, whilst the second is a non-interacting scalar field (phi) with an exponential potential V=Lambda exp(k phi). In particular, we study the asymptotic properties of the models both at early and late times, paying particular attention on whether the models isotropize (and inflate) to the future, and we discuss the genericity of the cosmological scaling solutions.

gr-qc↗
arXiv1999

A complete classification of spherically symmetric perfect fluid similarity solutions

We classify all spherically symmetric perfect fluid solutions of Einstein's equations with equation of state p/mu=a which are self-similar in the sense that all dimensionless variables depend only upon z=r/t. For a given value of a, such solutions are described by two parameters and they can be classified in terms of their behaviour at large and small distances from the origin; this usually corresponds to large and small values of z but (due to a coordinate anomaly) it may also correspond to finite z. We base our analysis on the demonstration that all similarity solutions must be asymptotic to solutions which depend on either powers of z or powers of lnz. We show that there are only three similarity solutions which have an exact power-law dependence on z: the flat Friedmann solution, a static solution and a Kantowski-Sachs solution (although the latter is probably only physical for a<0). For a>1/5, there are also two families of solutions which are asymptotically (but not exactly) Minkowski: the first is asymptotically Minkowski as z tends to infinity and is described by one parameter; the second is asymptotically Minkowski at a finite value of z and is described by two parameters. A complete analysis of the dust solutions is given, since these can be written down explicitly and elucidate the link between the z>0 and z<0 solutions. Solutions with pressure are then discussed in detail; these share many of the characteristics of the dust solutions but they also exhibit new features.

gr-qc↗
arXiv1998

The stability of cosmological scaling solutions

We study the stability of cosmological scaling solutions within the class of spatially homogeneous cosmological models with a perfect fluid subject to the equation of state p_gamma=(gamma-1) rho_gamma (where gamma is a constant satisfying 0 < gamma < 2) and a scalar field with an exponential potential. The scaling solutions, which are spatially flat isotropic models in which the scalar field energy density tracks that of the perfect fluid, are of physical interest. For example, in these models a significant fraction of the current energy density of the Universe may be contained in the scalar field whose dynamical effects mimic cold dark matter. It is known that the scaling solutions are late-time attractors (i.e., stable) in the subclass of flat isotropic models. We find that the scaling solutions are stable (to shear and curvature perturbations) in generic anisotropic Bianchi models when gamma < 2/3. However, when gamma > 2/3, and particularly for realistic matter with gamma >= 1, the scaling solutions are unstable; essentially they are unstable to curvature perturbations, although they are stable to shear perturbations. We briefly discuss the physical consequences of these results.

gr-qc↗
arXiv1998

Self-Similarity in General Relativity \endtitle

The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatially homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been completely classified, and we discuss various astrophysical and cosmological applications of such solutions. Finally we consider more general types of self-similar models.

gr-qc↗