arXiv subjects
Publications and source records attributed to A. A. Coley.
We use the 1+3 frame formalism to write down the evolution equations for spherically symmetric models as a well-posed system of first order PDEs in two variables, suitable for numerical and qualitative analysis.
The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the dynamics though correction (backreaction) terms, which can lead to behaviour qualitatively and quantitatively different from the Friedmann-Lemaître-Robertson-Walker models. The effects of averaging on cosmological observations are discussed. It is argued that, based on estimates from observational data, the backreaction (and, in particular, the averaged spatial curvature) can have a very significant dynamical effect on the evolution of the Universe and must be taken into account in observational cosmology.
We show that the higher-dimensional vanishing scalar invariant (VSI) spacetimes with fluxes and dilaton are solutions of type IIB supergravity, and we argue that they are exact solutions in string theory. We also discuss the supersymmetry properties of VSI spacetimes.
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of spherically symmetric cosmological models. That is, we shall take the microscopic equations and effect the averaging procedure to determine the precise form of the correlation tensor in this case. In particular, by working in volume preserving coordinates, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. We find that the correlation tensor in a FLRW background must be of the form of a spatial curvature. Inhomogeneities and spatial averaging, through this spatial curvature correction term, can have a very significant dynamical effect on the dynamics of the Universe and cosmological observations; in particular, we discuss whether spatial averaging might lead to a more conservative explanation of the observed acceleration of the Universe (without the introduction of exotic dark matter fields). We also find that the correlation tensor for a non-FLRW background can be interpreted as the sum of a spatial curvature and an anisotropic fluid. This may lead to interesting effects of averaging on astrophysical scales. We also discuss the results of averaging an inhomogeneous Lemaitre-Tolman-Bondi solution as well as calculations of linear perturbations (that is, the back-reaction) in an FLRW background, which support the main conclusions of the analysis.
We investigate the effect of dark energy on the limits on the shear anisotropy in spatially homogeneous Bianchi cosmological models obtained from measurements of the temperature anisotropies in the cosmic microwave background. We shall primarily assume that the dark energy is modelled by a cosmological constant. In general, we find that there are tighter bounds on the shear than in models with no cosmological constant, although the limits are (Bianchi) model dependent. In addition, there are special spatially homogeneous cosmological models whose rate of expansion is highly anisotropic, but whose cosmic microwave background temperature is measured to be exactly isotropic at one instant of time.
We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cosmologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are asymptotically null with respect to each other, their respective Weyl parameters generally both tend to zero, constant, or infinity together. We examine three classes of typical examples and one exceptional class. Given the behaviour of the Weyl parameter, we can predict that the singularity encountered is a Weyl singularity or a kinematic singularity. The analysis suggests that the kinematic variables are also useful in indicating a singularity in these models.
We show that in tilting perfect fluid cosmological models with an ultra-radiative equation of state, generically the tilt becomes extreme at late times and, as the tilt instability sets in, observers moving with the tilting fluid will experience singular behaviour in which infinite expansion is reached within a finite proper time, similar to that of phantom cosmology (but without the need for exotic forms of matter).
We discuss the averaging problem in general relativity, using the form of the macroscopic gravity equations in the case of spherical symmetry in volume preserving coordinates. In particular, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. On cosmological scales, the correlation tensor in a Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) background is found to be of the form of a spatial curvature. On astrophysical scales the correlation tensor can be interpreted as the sum of a spatial curvature and an anisotropic fluid. We briefly discuss the physical implications of these results.
We study perfect fluid cosmological models with a constant equation of state parameter $γ$ in which there are two naturally defined time-like congruences, a geometrically defined geodesic congruence and a non-geodesic fluid congruence. We establish an appropriate set of boost formulae relating the physical variables, and consequently the observed quantities, in the two frames. We study expanding spatially homogeneous tilted perfect fluid models, with an emphasis on future evolution with extreme tilt. We show that for ultra-radiative equations of state (i.e., $γ>4/3$), generically the tilt becomes extreme at late times and the fluid observers will reach infinite expansion within a finite proper time and experience a singularity similar to that of the big rip. In addition, we show that for sub-radiative equations of state (i.e., $γ< 4/3$), the tilt can become extreme at late times and give rise to an effective quintessential equation of state. To establish the connection with phantom cosmology and quintessence, we calculate the effective equation of state in the models under consideration and we determine the future asymptotic behaviour of the tilting models in the fluid frame variables using the boost formulae. We also discuss spatially inhomogeneous models and tilting spatially homogeneous models with a cosmological constant.
We use expansion-normalised variables to investigate the Bianchi type VII$_0$ model with a tilted $γ$-law perfect fluid. We emphasize the late-time asymptotic dynamical behaviour of the models and determine their asymptotic states. Unlike the other Bianchi models of solvable type, the type VII$_0$ state space is unbounded. Consequently we show that, for a general non-inflationary perfect fluid, one of the curvature variables diverges at late times, which implies that the type VII$_0$ model is not asymptotically self-similar to the future. Regarding the tilt velocity, we show that for fluids with $γ<4/3$ (which includes the important case of dust, $γ=1$) the tilt velocity tends to zero at late times, while for a radiation fluid, $γ=4/3$, the fluid is tilted and its vorticity is dynamically significant at late times. For fluids stiffer than radiation ($γ>4/3$), the future asymptotic state is an extremely tilted spacetime with vorticity.
Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the equations of macroscopic gravity for a spatially homogeneous and isotropic macroscopic space-time and find that the correlation tensor is of the form of a spatial curvature term. We briefly discuss the physical consequences of these results.
This article has been removed. It has been superseded by gr-qc/0506097.
We calculate analytically the past asymptotic decay rates close to an initial singularity in general G_0 spatially inhomogeneous perfect fluid models with an effective equation of state which is stiff or ultra-stiff (i.e., $γ\ge 2$). These results are then supported by numerical simulations in a special class of G_2 cosmological models. Our analysis confirms and extends the BKL conjectures and lends support to recent isotropization results in cosmological models of current interest (with $γ> 2$).
Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or {\em brane} embedded in a higher-dimensional {\em bulk} spacetime. Ordinary matter fields are confined to the brane while the gravitational field can also propagate in the bulk, leading to modifications of Einstein's theory of general relativity at high energies. In particular, the Randall-Sundrum-type models are self-consistent and simple and allow for an investigation of the essential non-linear gravitational dynamics. The governing field equations induced on the brane differ from the general relativistic equations in that there are nonlocal effects from the free gravitational field in the bulk, transmitted via the projection of the bulk Weyl tensor, and the local quadratic energy-momentum corrections, which are significant in the high-energy regime close to the initial singularity. In this review we discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models containing both a perfect fluid and a scalar field close to the initial singularity. Using dynamical systems techniques it is found that, for models with a physically relevant equation of state, an isotropic singularity is a past-attractor in all orthogonal spatially homogeneous models (including Bianchi type IX models). In addition, we describe the dynamics in a class of inhomogeneous brane-world models, and show that these models also have an isotropic initial singularity. These results provide support for the conjecture that typically the initial cosmological singularity is isotropic in brane-world cosmology.
We discuss the asymptotic dynamical evolution of spatially inhomogeneous brane-world cosmological models close to the initial singularity. By introducing suitable scale-invariant dependent variables and a suitable gauge, we write the evolution equations of the spatially inhomogeneous $G_{2}$ brane cosmological models with one spatial degree of freedom as a system of autonomous first-order partial differential equations. We study the system numerically, and we find that there always exists an initial singularity, which is characterized by the fact that spatial derivatives are dynamically negligible. More importantly, from the numerical analysis we conclude that there is an initial isotropic singularity in all of these spatially inhomogeneous brane cosmologies for a range of parameter values which include the physically important cases of radiation and a scalar field source. The numerical results are supported by a qualitative dynamical analysis and a calculation of the past asymptotic decay rates. Although the analysis is local in nature, the numerics indicates that the singularity is isotropic for all relevant initial conditions. Therefore this analysis, and a preliminary investigation of general inhomogeneous ($G_0$) models, indicates that it is plausible that the initial singularity is isotropic in spatially inhomogeneous brane-world cosmological models and consequently that brane cosmology naturally gives rise to a set of initial data that provide the conditions for inflation to subsequently take place.
We use the cosmic microwave background temperature anisotropy to place limits on large-scale magnetic fields in an inhomogeneous (perturbed Friedmann) universe. If no assumptions are made about the spacetime geometry, only a weak limit can be deduced directly from the CMB. In the special case where spatial inhomogeneity is neglected to first order, the upper limit is much stronger, i.e. a few nano-G
We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave background. We discuss multi-fluid models, and illustrate how more general inhomogeneous models may be derived, both in General Relativity and in scalar-tensor theories of gravity. Thus we illustrate that the cosmological principle, the assumption that the Universe we live in is spatially homogeneous, does not necessarily follow from the Copernican principle and the high isotropy of the cosmic microwave background.