arXiv subjects

Alan Coley

Publications and source records attributed to Alan Coley.

50 records · Page 3Linked to original sources

arXiv2009

Lorentzian spacetimes with constant curvature invariants in four dimensions

In this paper we investigate four dimensional Lorentzian spacetimes with constant curvature invariants ($CSI$ spacetimes). We prove that if a four dimensional spacetime is $CSI$, then either the spacetime is locally homogeneous or the spacetime is a Kundt spacetime for which there exists a frame such that the positive boost weight components of all curvature tensors vanish and the boost weight zero components are all constant. We discuss some of the properties of the Kundt-$CSI$ spacetimes and their applications. In particular, we discuss $\mathcal{I}$-symmetric spaces and degenerate Kundt $CSI$ spacetimes.

gr-qc↗

arXiv2008

Lorentzian spacetimes with constant curvature invariants in three dimensions

In this paper we study Lorentzian spacetimes for which all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives are constant (CSI spacetimes) in three dimensions. We determine all such CSI metrics explicitly, and show that for every CSI with particular constant invariants there is a locally homogeneous spacetime with precisely the same constant invariants. We prove that a three-dimensional CSI spacetime is either (i) locally homogeneous or (ii) it is locally a Kundt spacetime. Moreover, we show that there exists a null frame in which the Riemann (Ricci) tensor and its derivatives are of boost order zero with constant boost weight zero components at each order. Lastly, these spacetimes can be explicitly constructed from locally homogeneous spacetimes and vanishing scalar invariant spacetimes.

gr-qc↗

arXiv2006

On Spacetimes with Constant Scalar Invariants

We study Lorentzian spacetimes for which all scalar invariants constructed from the Riemann tensor and its covariant derivatives are constant ($CSI$ spacetimes). We obtain a number of general results in arbitrary dimensions. We study and construct warped product $CSI$ spacetimes and higher-dimensional Kundt $CSI$ spacetimes. We show how these spacetimes can be constructed from locally homogeneous spaces and $VSI$ spacetimes. The results suggest a number of conjectures. In particular, it is plausible that for $CSI$ spacetimes that are not locally homogeneous the Weyl type is $II$, $III$, $N$ or $O$, with any boost weight zero components being constant. We then consider the four-dimensional $CSI$ spacetimes in more detail. We show that there are severe constraints on these spacetimes, and we argue that it is plausible that they are either locally homogeneous or that the spacetime necessarily belongs to the Kundt class of $CSI$ spacetimes, all of which are constructed. The four-dimensional results lend support to the conjectures in higher dimensions.

gr-qc↗

arXiv2005

Inhomogeneous perturbations of plane-wave spacetimes

Recently it was shown that the exact cosmological solutions known as the vacuum plane-wave solutions are late-time attractors for an open set of the spatially homogeneous Bianchi universes containing a non-inflationary $γ$-law perfect fluid. In this paper we study inhomogeneous perturbations of these plane-wave spacetimes. By using expansion-normalised scale-invariant variables we show that these solutions are unstable to generic inhomogeneous perturbations. The crucial observation for establishing this result is a divergence of the expansion-normalised frame variables which ultimately leads to unstable modes.

gr-qc↗

arXiv2005

Are braneworlds born isotropic?

It has recently been suggested that an isotropic singularity may be a generic feature of brane cosmologies, even in the inhomogeneous case. Using the covariant and gauge-invariant approach we present a detailed analysis of linear perturbations of the isotropic model ${\cal F}_b$ which is a past attractor in the phase space of homogeneous Bianchi models on the brane. We find that for matter with an equation of state parameter $γ> 1$, the dimensionless variables representing generic anisotropic and inhomogeneous perturbations decay as $t\to 0$, showing that the model ${\cal F}_b$ is asymptotically stable in the past. We conclude that brane universes are born with isotropy naturally built-in, contrary to standard cosmology. The observed large-scale homogeneity and isotropy of the universe can therefore be explained as a consequence of the initial conditions if the brane-world paradigm represents a description of the very early universe.

hep-th↗

arXiv2004

Gravitational entropy in cosmological models

We discuss whether an appropriately defined dimensionless scalar function might be an acceptable candidate for the gravitational entropy, by explicitly considering Szekeres and Bianchi type VI$_{h}$ models that admit an isotropic singularity. We also briefly discuss other possible gravitational entropy functions, including an appropriate measure of the velocity dependent Bel-Robinson tensor.

gr-qc↗

arXiv2004

Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh

Using dynamical systems theory and a detailed numerical analysis, the late-time behaviour of tilting perfect fluid Bianchi models of types IV and VII$_h$ are investigated. In particular, vacuum plane-wave spacetimes are studied and the important result that the only future attracting equilibrium points for non-inflationary fluids are the plane-wave solutions in Bianchi type VII$_h$ models is discussed. A tiny region of parameter space (the loophole) in the Bianchi type IV model is shown to contain a closed orbit which is found to act as an attractor (the Mussel attractor). From an extensive numerical analysis it is found that at late times the normalised energy-density tends to zero and the normalised variables 'freeze' into their asymptotic values. A detailed numerical analysis of the type VII$_h$ models then shows that there is an open set of parameter space in which solution curves approach a compact surface that is topologically a torus.

gr-qc↗

arXiv2004

A dynamical systems approach to the tilted Bianchi models of solvable type

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VI$_h$ and VII$_h$) with a perfect fluid and a linear barotropic $γ$-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi VII$_0$ models. We prove the important result that for non-inflationary Bianchi type VII$_h$ models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VII$_h$ invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exists closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VII$_h$ models there is a bifurcation in which a set of equilibrium points turn into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VII$_h$ models in this region the solution curves approach a compact surface which is topologically a torus.

gr-qc↗

arXiv2004

Large-scale perturbations on the brane and the isotropy of the cosmological singularity

We present the complete set of propagation and constraint equations for the kinematic and non-local first order quantities which describe general linear inhomogeneous and anisotropic perturbations of a flat FRW braneworld with vanishing cosmological constant and decompose them in the standard way into their scalar, vector and tensor contributions. A detailed analysis of the perturbation dynamics is performed using dimensionless variables that are specially tailored for the different regimes of interest; namely, the low energy GR regime, the high energy regime and the dark energy regime. Tables are presented for the evolution of all the physical quantities, making it easy to do a detailed comparison of the past asymptotic behaviour of the perturbations of these models. We find results that exactly match those obtained in the analysis of the spatially inhomogeneous $G_{2}$ braneworld cosmologies presented recently; i.e., that isotropization towards the ${\cal F}_b$ model occurs for $γ> 4/3$.

hep-th↗

arXiv2003

Isotropic singularity in brane cosmological models

It is argued that the initial cosmological singularity is isotropic in spatially inhomogeneous brane-world models. This implies that brane cosmology may naturally give rise to a set of initial data that provide the conditions for inflation to subsequently take place, consequently offering a plausible solution to the initial conditions problem in cosmology.

gr-qc↗

arXiv2003

Scaling solution, radion stabilization, and initial condition for brane-world cosmology

We propose a new, self-consistent and dynamical scenario which gives rise to well-defined initial conditions for five-dimensional brane-world cosmologies with radion stabilization. At high energies, the five-dimensional effective theory is assumed to have a scale invariance so that it admits an expanding scaling solution as a future attractor. The system automatically approaches the scaling solution and, hence, the initial condition for the subsequent low-energy brane cosmology is set by the scaling solution. At low energies, the scale invariance is broken and a radion stabilization mechanism drives the dynamics of the brane-world system. We present an exact, analytic scaling solution for a class of scale-invariant effective theories of five-dimensional brane-world models which includes the five-dimensional reduction of the Horava-Witten theory, and provide convincing evidence that the scaling solution is a future attractor.

hep-th↗

arXiv2002

Averaging out Inhomogeneous Newtonian Cosmologies: III. The Averaged Navier-Stokes-Poisson Equations

The basic concepts and hypotheses of Newtonian Cosmology necessary for a consistent treatment of the averaged cosmological dynamics are formulated and discussed in details. The space-time, space, time and ensemble averages for the cosmological fluid fields are defined and analyzed with a special attention paid to their analytic properties. It is shown that all averaging procedures require an arrangement for a standard measurement device with the same measurement time interval and the same space region determined by the measurement device resolution to be prescribed to each position and each moment of time throughout a cosmological fluid configuration. The formulae for averaging out the partial derivatives of the averaged cosmological fluid fields and the main formula for averaging out the material derivatives have been proved. The full system of the averaged Navier-Stokes-Poisson equations in terms of the fluid kinematic quantities is derived.

gr-qc↗

arXiv2000

Closed cosmologies with a perfect fluid and a scalar field

Closed, spatially homogeneous cosmological models with a perfect fluid and a scalar field with exponential potential are investigated, using dynamical systems methods. First, we consider the closed Friedmann-Robertson-Walker models, discussing the global dynamics in detail. Next, we investigate Kantowski-Sachs models, for which the future and past attractors are determined. The global asymptotic behaviour of both the Friedmann-Robertson-Walker and the Kantowski-Sachs models is that they either expand from an initial singularity, reach a maximum expansion and thereafter recollapse to a final singularity (for all values of the potential parameter kappa), or else they expand forever towards a flat power-law inflationary solution (when kappa^2<2). As an illustration of the intermediate dynamical behaviour of the Kantowski-Sachs models, we examine the cases of no barotropic fluid, and of a massless scalar field in detail. We also briefly discuss Bianchi type IX models.

gr-qc↗

arXiv2000

Self-similar spherically symmetric cosmological models with a perfect fluid and a scalar field

Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are utilised to analyse the models. Due to the existence of monotone functions global dynamical results can be deduced. In particular, all of the future and past attractors for these models are obtained and the global results are discussed. The essential physical results are that initially expanding models always evolve away from a massless scalar field model with an initial singularity and, depending on the parameters of the models, either recollapse to a second singularity or expand forever towards a flat power-law inflationary model. The special cases in which there is no barotropic fluid and in which the scalar field is massless are considered in more detail in order to illustrate the asymptotic results. Some phase portraits are presented and the intermediate dynamics and hence the physical properties of the models are discussed.

gr-qc↗