arXiv subjects

Alan A. Coley

Publications and source records attributed to Alan A. Coley.

31 records · Page 2Linked to original sources

arXiv2004

Bianchi Cosmologies: A Tale of Two Tilted fluids

We use a dynamical systems approach to study Bianchi type VI$_0$ cosmological models containing two tilted $γ$-law perfect fluids. The full state space is 11-dimensional, but the existence of a monotonic function simplifies the analysis considerably. We restrict attention to a particular, physically interesting, invariant subspace and find all equilibrium points that are future stable in the full 11-dimensional state space; these are consequently local attractors and serve as late-time asymptotes for an open set of tilted type VI$_0$ models containing two tilted fluids. We find that if one of the fluids has an equation of state parameter $γ<6/5$, the stiffest fluid will be dynamically insignificant at late times. For the value $γ=6/5$ there is a 2-dimensional bifurcation set, and if both fluids are stiffer than $γ=6/5$ both fluids will have extreme tilt asymptotically. We investigate the case in which one fluid is extremely tilting in detail. We also consider the case with one stiff fluid ($γ=2$) close to the initial singularity, and find that the chaotic behaviour which occurs in general Bianchi models with $γ<2$ is suppressed.

gr-qc↗

arXiv2003

Brane-world Singularities

We study the behavior of spatially homogeneous brane-worlds close to the initial singularity in the presence of both local and nonlocal stresses. It is found that the singularity in these brane-worlds can be locally either isotropic or anisotropic. We then investigate the Weyl curvature conjecture, according to which some measure of the Weyl curvature is related to a gravitational entropy. In particular, we study the Weyl curvature conjecture on the brane with respect to the dimensionless ratio of the Weyl invariant and the Ricci square and the measure proposed by Grøn and Hervik. We also argue that the Weyl curvature conjecture should be formulated on brane (i.e., in the four-dimensional context).

gr-qc↗

arXiv2002

A qualitative and numerical study or the matter-radiation interaction in Kantowski-Sachs cosmologies

We examine, from both a qualitative and a numerical point of view, the evolution of Kantowski--Sachs cosmological models whose source is a mixture of a gas of weakly interacting massive particles (WIMP's) and a radiative gas made up of a ``tightly coupled'' mixture of electrons, baryons and photons from the end of nucleosynthesis up to the duration of radiative interactions. In this cosmic era annihilation processes are negligible, while the WIMP's only interact gravitationally with the radiative gas and the latter behaves as a single dissipative fluid that can be studied within a hydrodynamical framework. Applying the full transport equations of Extended Irreversible Thermodynamics, coupled with the field and balance equations, we obtain a set of governing equations that becomes an autonomous system of ordinary differential equations once the shear viscosity relaxation time is specified; assuming the latter to be proportional to the Hubble time, the qualitative analysis indicates that models begin in the radiation dominated epoch close to an isotropic equilibrium point. We show how the relaxation time governs the relaxation of the models towards an equilibrium photon entropy, leading to ``near-Eckart'' and transient regimes associated with `abrupt' and `smooth' relaxation processes, respectively. Assuming the WIMP particle to be a super-symmetric neutralino of a 100$ GeV, the numerical analysis reveals that a physically plausible evolution, compatible with a stable equilibrium state and with observed bounds on CMB anisotropies and neutralino abundance, is only possible for models characterized by initial conditions associated with nearly zero spatial curvature and total initial energy density very close to unity.

astro-ph↗

arXiv2002

Inhomogeneous M-Theory Cosmologies

We study a class of inhomogeneous and anisotropic $G_2$ string cosmological models. In the case of separable $G_2$ models we show that the governing equations reduce to a system of ordinary differential equations. We focus on a class of separable $G_2$ M-theory cosmological models, and study their qualitative behaviour (a class of models with time-reversed dynamics is also possible). We find that generically these inhomogeneous M-theory cosmologies evolve from a spatially inhomogeneous and negatively curved model with a non-trivial form field towards spatially flat and spatially homogeneous dilaton-moduli-vacuum solutions with trivial form--fields. The late time behaviour is the same as that of spatially homogeneous models previously studied. However, the inhomogeneities are not dynamically insignificant at early times in these models.

hep-th↗

arXiv2001

Infinite Kinematic Self-Similarity and Perfect Fluid Spacetimes

Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary differential equations. The qualitative properties of solutions of this system of equations, and in particular their asymptotic behavior, are studied. Special cases, including some of the invariant sets and the geodesic case, are examined in detail and the exact solutions are provided. The class of solutions exhibiting physical self-similarity are found to play an important role in describing the asymptotic behavior of the infinite kinematic self-similar models.

gr-qc↗

arXiv2000

Cyclical Behaviour in Early Universe Cosmologies

We study early universe cosmologies derived from a scalar-tensor action containing cosmological constant terms and massless fields. The governing equations can be written as a dynamical system which contains no past or future asymptotic equilibrium states (i.e. no sources nor sinks). This leads to dynamics with very interesting mathematical behaviour such as the existence of heteroclinic cycles. The corresponding cosmologies have novel characteristics, including cyclical and bouncing behaviour possibly indicating chaos. We discuss the connection between these early universe cosmologies and those derived from the low-energy string effective action.

gr-qc↗

arXiv1999

Qualitative Analysis of Isotropic Curvature String Cosmologies

A complete qualitative study of the dynamics of string cosmologies is presented for the class of isotopic curvature universes. These models are of Bianchi types I, V and IX and reduce to the general class of Friedmann-Robertson-Walker universes in the limit of vanishing shear isotropy. A non-trivial two-form potential and cosmological constant terms are included in the system. In general, the two-form potential and spatial curvature terms are only dynamically important at intermediate stages of the evolution. In many of the models, the cosmological constant is important asymptotically and anisotropy becomes dynamically negligible. There also exist bouncing cosmologies.

hep-th↗

arXiv1999

Interactions in Scalar Field Cosmology

We investigate spatially flat isotropic cosmological models which contain a scalar field with an exponential potential and a perfect fluid with a linear equation of state. We include an interaction term, through which the energy of the scalar field is transferred to the matter fields, consistent with a term that arises from scalar--tensor theory under a conformal transformation and field redefinition. The governing ordinary differential equations reduce to a dynamical system when appropriate normalized variables are defined. We analyse the dynamical system and find that the interaction term can significantly affect the qualitative behaviour of the models. The late-time behaviour of these models may be of cosmological interest. In particular, for a specific range of values for the model parameters there are late-time attracting solutions, corresponding to a novel attracting equilib rium point, which are inflationary and in which the scalar field's energy-density remains a fixed fraction of the matter field's energy density. These scalar field models may be of interest as late-time cosmologies, part icularly in view of the recent observations of the current accelerated cosmic expansion. For appropriate values of the interaction coupling parameter, this equilibrium point is an attracting focus, and hence as inflating solutions approach this late-time attractor the scalar field oscillates. Hence these models may also be of importance in the study of inflation in the early universe.

astro-ph↗

arXiv1999

Dynamics of M-Theory Cosmology

A complete global analysis of spatially-flat, four-dimensional cosmologies derived from the type IIA string and M-theory effective actions is presented. A non--trivial Ramond-Ramond sector is included. The governing equations are written as a dynamical system. Asymptotically, the form fields are dynamically negligible, but play a crucial role in determining the possible intermediate behaviour of the solutions (i.e. the nature of the equilibrium points). The only past-attracting solution (source in the system) may be interpreted in the eleven-dimensional setting in terms of flat space. This source is unstable to the introduction of spatial curvature.

hep-th↗

arXiv1999

Qualitative Analysis of String Cosmologies

A qualitative analysis is presented for spatially flat, isotropic and homogeneous cosmologies derived from the string effective action when the combined effects of a dilaton, modulus, two-form potential and central charge deficit are included. The latter has significant effects on the qualitative dynamics. The analysis is also directly applicable to the anisotropic Bianchi type I cosmology.

gr-qc↗

arXiv1999

Scaling Solutions in Robertson-Walker Spacetimes

We investigate the stability of cosmological scaling solutions describing a barotropic fluid with $p=(γ-1)ρ$ and a non-interacting scalar field $ϕ$ with an exponential potential $V(ϕ)=V_0\e^{-κϕ}$. We study homogeneous and isotropic spacetimes with non-zero spatial curvature and find three possible asymptotic future attractors in an ever-expanding universe. One is the zero-curvature power-law inflation solution where $Ω_ϕ=1$ ($γ<2/3,κ^2<3γ$ and $γ>2/3,κ^2<2$). Another is the zero-curvature scaling solution, first identified by Wetterich, where the energy density of the scalar field is proportional to that of matter with $Ω_ϕ=3γ/κ^2$ ($γ<2/3,κ^2>3γ$). We find that this matter scaling solution is unstable to curvature perturbations for $γ>2/3$. The third possible future asymptotic attractor is a solution with negative spatial curvature where the scalar field energy density remains proportional to the curvature with $Ω_ϕ=2/κ^2$ ($γ>2/3,κ^2>2$). We find that solutions with $Ω_ϕ=0$ are never late-time attractors.

gr-qc↗

arXiv1994

On Spacetimes Admitting Shear-free, Irrotational, Geodesic Timelike Congruences

A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down. Coordinates in which the metric of such spacetimes takes on a simplified form are established. The general subcases of `zero anisotropic stress', `zero heat flux vector' and `two component fluids' are investigated. In particular, perfect fluid Friedmann-Robertson-Walker models and spatially homogeneous models are discussed. Models with a variety of physically relevant energy-momentum tensors are considered. Anisotropic fluid models and viscous fluid models with heat conduction are examined. Also, models with a perfect fluid plus a magnetic field or with pure radiation, and models with two non-collinear perfect fluids (satisfying a variety of physical conditions) are investigated. In particular, models with a (single) perfect fluid which is tilting with respect to the shear-free, vorticity-free and acceleration-free timelike congruence are discussed.

gr-qc↗

arXiv1994

Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress-tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a comoving observer, satisfy an equation of state of the form $p = p(μ)$, with $\frac{dp}{dμ} \neq -\frac{1}{3}$, then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.

gr-qc↗