Cosmic No Hair for Collapsing Universes

It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic universe in the neighbourhood of the big crunch singularity. This result is employed to investigate the asymptotic dynamics of a collapsing Bianchi type IX universe sourced by a scalar field rolling down a steep, negative exponential potential. A toroidally compactified version of M*-theory that leads to such a potential is discussed and it is shown that the isotropic attractor solution for a collapsing Bianchi type IX universe is supersymmetric when interpreted in an eleven-dimensional context.Comment: Extended discussion to include Kantowski-Sachs universe. In press, Classical and Quantum Gravit

Self-similar Bianchi models: I. Class A models

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration constants. We apply the geometrical results for tilted perfect fluids sources and give the general Bianchi II self-similar solution and the form of the similarity vector field. In addition we show that self-similar perfect fluid Bianchi VII$_0$ models and irrotational Bianchi VI$_0$ models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit

Bianchi VIII Empty Futures

Using a qualitative analysis based on the Hamiltonian formalism and the orthonormal frame representation we investigate whether the chaotic behaviour which occurs close to the initial singularity is still present in the far future of Bianchi VIII models. We describe some features of the vacuum Bianchi VIII models at late times which might be relevant for studying the nature of the future asymptote of the general vacuum inhomogeneous solution to the Einstein field equations.Comment: 22 pages, no figures, Latex fil

Design and performance of a multicentre, randomized controlled trial of teleconsulting.

We have designed and performed a multicentre, randomized controlled trial of teleconsulting. The trial investigated the effectiveness and cost implications in rural and inner-city settings of using videoconferencing as an alternative to general practitioner referral to a hospital specialist. The participating general practitioners referred a total of 3170 patients who satisfied the entry criteria. Of these, 1040 (33%) failed to provide consent or otherwise refused to participate in the trial. Of the patients recruited to the trial, a total of 1902 (91%) completed and returned the baseline questionnaire. Although the trial was successful in recruiting sufficient patients and in obtaining high questionnaire response rates, the findings will require careful interpretation to take account of the limits which the protocol placed on the ability of general practitioners to select patients for referral

Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric

The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states of the spacetimes near the singularity or in a phase of unlimited expansion. Bianchi type II models show oscillatory behaviour near the initial singularity which is, however, simpler than that of the mixmaster model.Comment: 27 pages, 3 figures, LaTe

Joint teleconsultations (virtual outreach) versus standard outpatient appointments for patients referred by their general practitioner for a specialist opinion: a randomised trial.

BACKGROUND: The current model of general practitioner referral of patients to hospital specialists in the UK is sometimes associated with unnecessary duplication of investigations and treatments. We aimed to compare joint teleconsultations between general practitioners, specialists, and patients (virtual outreach) with standard outpatient referral. METHODS: Virtual outreach services were established in London and Shrewsbury. The general practitioners referred 3170 patients, of whom 2094 consented to participate in the study and were eligible for inclusion. 1051 patients were randomly assigned virtual outreach, and 1043 standard outpatient appointments. We followed up the patients for 6 months after their index consultation. The primary outcome measure was the offer of a follow-up outpatient appointment. Analysis was by intention to treat. FINDINGS: More patients in the virtual outreach group than the standard group were offered a follow-up appointment (502 [52%] vs 400 [41%], odds ratio 1.52 [95% CI 1.27-1.82], p<0.0001). Significant differences in effects were observed between the two sites (p=0.009) and across different specialties (p<0.0001). Virtual outreach increased the offers of follow-up appointments more in Shrewsbury than in London, and more in ear, nose, and throat surgery and orthopaedics than in the other specialties. Fewer tests and investigations were ordered in the virtual outreach group by an average of 0.79 per patient (0.37-1.21, p=0.0002). Patients' satisfaction (analysed per protocol) was greater after a virtual outreach consultation than after a standard outpatient consultation (mean difference 0.33 scale points [95% CI 0.23-0.43], p<0.0001), with no heterogeneity between specialties or sites. INTERPRETATION: The trial showed that allocation of patients to virtual outreach consultations is variably associated with increased offers of follow-up appointments according to site and specialty, but leads to significant increases in patients' satisfaction and substantial reductions in tests and investigations. Efficient operation of such services will require appropriate selection of patients, significant service reorganisation, and provision of logistical support

Global dynamics of the mixmaster model

The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for solutions of types other than VIII and IX the singularity is velocity dominated and that the Kretschmann scalar is unbounded there, except in the explicitly known cases where the spacetime can be smoothly extended through a Cauchy horizon. For types VIII and IX it is shown that there are at most two possibilities for the evolution. When the first possibility is realized, and if the spacetime is not one of the explicitly known solutions which can be smoothly extended through a Cauchy horizon, then there are infinitely many oscillations near the singularity and the Kretschmann scalar is unbounded there. The second possibility remains mysterious and it is left open whether it ever occurs. It is also shown that any finite sequence of distinct points generated by iterating the Belinskii-Khalatnikov-Lifschitz mapping can be realized approximately by a solution of the vacuum Einstein equations of Bianchi type IX.Comment: 16 page

Cylindrically symmetric dust spacetime

We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has new surprising features. The universe is ``closed'' in the sense that the dust expands from a big-bang singularity but recollapses to a big-crunch singularity. In fact, both singularities are connected so that the whole spacetime is ``enclosed'' within a single singularity of general character. The big-bang is not simultaneous for the dust, and in fact the age of the universe as measured by the dust particles depends on the spatial position, an effect due to the inhomogeneity, and their total lifetime has no non-zero lower limit. Part of the big-crunch singularity is naked. The metric depends on a parameter and contains flat spacetime as a non-singular particular case. For appropriate values of the parameter the spacetime is a small perturbation of Minkowski spacetime. This seems to indicate that flat spacetime may be unstable against some global {\it non-vacuum} perturbations.Comment: LaTeX, 6 pages, 1 figure. Uses epsfig package. Submitted to Classical and Quantum Gravit

Integration of the Friedmann equation for universes of arbitrary complexity

An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of the motion from simpler models as more species are added is stressed. It is then argued that all FLRW models admit what amounts to a unique candidate for a gravitational epoch function (a dimensionless scalar invariant derivable from the Riemann tensor without differentiation which is monotone throughout the evolution of the universe). The same relations that lead to the construction of constants of the motion allow an explicit evaluation of this function. In the simplest of all models, the $\Lambda$CDM model, it is shown that the epoch function exists for all models with $\Lambda > 0$, but for almost no models with $\Lambda \leq 0$.Comment: Final form to appear in Physical Review D1

Homogeneous cosmologies with cosmological constant

Spatially homogeneous cosmological models with a positive cosmological constant are investigated, using dynamical systems methods. We focus on the future evolution of these models. In particular, we address the question whether there are models within this class that are de Sitter-like in the future, but are tilted.Comment: 10 pages, 13 eps-figures. Submitted to Phys. Rev.