Computing Gowdy spacetimes via spectral evolution in future and past directions

We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy symmetric spacetimes on T3. We introduce two numerical methods, which are based on pseudo-spectral approximation. The first approach relies on marching in the future time-like direction and toward the coordinate singularity t=0. The second approach is designed from asymptotic formulas that are available near this singularity; it evolves the solutions in the past timelike direction from "final" data given at t=0. This backward method relies a novel nonlinear transformation, which allows us to reduce the nonlinear source terms to simple quadratic products of the unknown variables. Numerical experiments are presented in various regimes, including cases where "spiky" structures are observed as the coordinate singularity is approached. The proposed backward strategy leads to a robust numerical method which allows us to accurately simulate the long-time behavior of a large class of Gowdy spacetimes.Comment: 19 pages, 12 figure

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

The problem of a self-gravitating scalar field with positive cosmological constant

We study the Einstein-scalar field system with positive cosmological constant and spherically symmetric characteristic initial data given on a truncated null cone. We prove well-posedness, global existence and exponential decay in (Bondi) time, for small data. From this, it follows that initial data close enough to de Sitter data evolves to a causally geodesically complete spacetime (with boundary), which approaches a region of de Sitter asymptotically at an exponential rate; this is a non-linear stability result for de Sitter within the class under consideration, as well as a realization of the cosmic no-hair conjecture.We thank Pedro Girao, Marc Mars, Alan Rendall, Jorge Silva and Raul Vera for useful discussions. This work was supported by projects PTDC/MAT/108921/2008 and CERN/FP/116377/2010, and by CMAT, Universidade do Minho, and CAMSDG, Instituto Superior Tecnico, through FCT plurianual funding. AA thanks the Mathematics Department of Instituto Superior Tecnico (Lisbon), where this work was done, and the International Erwin Schrodinger Institute (Vienna), where the workshop "Dynamics of General Relativity: Analytical and Numerical Approaches" took place, for hospitality, and FCT for grant SFRH/BD/48658/2008

A protocol for a trial of homeopathic treatment for irritable bowel syndrome

Background Irritable bowel syndrome is a chronic condition with no known cure. Many sufferers seek complementary and alternative medicine including homeopathic treatment. However there is much controversy as to the effectiveness of homeopathic treatment. This three-armed study seeks to explore the effectiveness of individualised homeopathic treatment plus usual care compared to both an attention control plus usual care and usual care alone, for patients with irritable bowel syndrome. Methods/design This is a three-armed pragmatic randomised controlled trial using the cohort multiple randomised trial methodology. Patients are recruited to an irritable bowel syndrome cohort from primary and secondary care using GP databases and consultants lists respectively. From this cohort patients are randomly selected to be offered, 5 sessions of homeopathic treatment plus usual care, 5 sessions of supportive listening plus usual care or usual care alone. The primary clinical outcome is the Irritable Bowel Syndrome Symptom Severity at 26 weeks. From a power calculation, it is estimated that 33 people will be needed for the homeopathic treatment arm and 132 for the usual care arm, to detect a minimal clinical difference at 80 percent power and 5 percent significance allowing for loss to follow up. An unequal group size has been used for reasons of cost. Analysis will be by intention to treat and will compare homeopathic treatment with usual care at 26 weeks as the primary analysis, and homeopathic treatment with supportive listening as an additional analysis. Discussion This trial has received NHS approval and results are expected in 2013. Trial registration Current Controlled Trials ISRCTN9065114