Kasner and Mixmaster behavior in universes with equation of state w \ge 1

We consider cosmological models with a scalar field with equation of state $w\ge 1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed, and the contraction is described by a homogeneous and isotropic Friedmann equation if $w>1$. We generalize the results to theories where the scalar field couples to p-forms and show that there exists a finite value of $w$, depending on the p-forms, such that chaotic oscillations are suppressed. We show that $Z_2$ orbifold compactification also contributes to suppressing chaotic behavior. In particular, chaos is avoided in contracting heterotic M-theory models if $w>1$ at the crunch.Comment: 25 pages, 2 figures, minor changes, references adde

Spacelike Singularities and Hidden Symmetries of Gravity

We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms of billiard motion in a region of hyperbolic space, revealing that the dynamics is completely determined by a (possibly infinite) sequence of reflections, which are elements of a Lorentzian Coxeter group. Such Coxeter groups are the Weyl groups of infinite-dimensional Kac-Moody algebras, suggesting that these algebras yield symmetries of gravitational theories. Our presentation is aimed to be a self-contained and comprehensive treatment of the subject, with all the relevant mathematical background material introduced and explained in detail. We also review attempts at making the infinite-dimensional symmetries manifest, through the construction of a geodesic sigma model based on a Lorentzian Kac-Moody algebra. An explicit example is provided for the case of the hyperbolic algebra E10, which is conjectured to be an underlying symmetry of M-theory. Illustrations of this conjecture are also discussed in the context of cosmological solutions to eleven-dimensional supergravity.Comment: 228 pages. Typos corrected. References added. Subject index added. Published versio

Earliest land plants created modern levels of atmospheric oxygen

The progressive oxygenation of the Earth’s atmosphere was pivotal to the evolution of life, but the puzzle of when and how atmospheric oxygen (O2) first approached modern levels (~21%) remains unresolved. Redox proxy data indicate the deep oceans were oxygenated during 435-392 Ma, and the appearance of fossil charcoal indicates O2>15-17% by 420-400 Ma. However, existing models have failed to predict oxygenation at this time. Here we show that the earliest plants, which colonized the land surface from ~470 Ma onwards, were responsible for this mid- Paleozoic oxygenation event, through greatly increasing global organic carbon burial – the net long-term source of O2. We use a trait-based ecophysiological model to predict that cryptogamic vegetation cover could have achieved ~30% of today’s global terrestrial net primary productivity by~445 Ma. Data from modern bryophytes suggests this plentiful early plant material had a much higher molar C:P ratio (~2000) than marine biomass (~100), such that a given weathering flux of phosphorus could support more organic carbon burial. Furthermore, recent experiments suggest that early plants selectively increased the flux of phosphorus (relative to alkalinity) weathered from rocks. Combining these effects in a model of long-term biogeochemical cycling, we reproduce a sustained +2‰ increase in the carbonate carbon isotope (δ13C) record by ~445 Ma, and predict a corresponding rise in O2 to present levels by 420-400 Ma, consistent with geochemical data. This oxygen rise represents a permanent shift in regulatory regime to one where fire-mediated negative feedbacks on organic carbon burial stabilise high O2 levels

The Bianchi Ix (MIXMASTER) Cosmological Model is Not Integrable

The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the perturbative Painlev\'e test; this proves the inexistence of any vacuum solution other than the three known ones.Comment: 14 pages, no figure

Adiabatic invariants and Mixmaster catastrophes

We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical results. We also present a new formulation of the dynamics via Catastrophe Theory. We find that the change from one era to the next corresponds to a fold catastrophe, during the Kasner shifts the potential is an Implicit Function Form whereas, as the anisotropy dissipates, the Mixmaster potential must become a Morse 0--saddle. We compare and contrast our results to many known works on the Mixmaster problem and indicate how extensions could be achieved. Further exploitation of this formulation may lead to a clearer understanding of the global Mixmaster dynamics.Comment: 24 pages, LaTeX, 5 figures (which can be obtained by sending a message to the first author), submitted to Phys.Rev.

Higher-Derivative Quantum Cosmology

The quantum cosmology of a higher-derivative derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler-DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques for solving the Wheeler-DeWitt equation with appropriate boundary conditions shall be described, and implications for semiclassical theories of inflationary cosmology will be outlined.Comment: 11 pages TeX. A term has been removed from equation (13

Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1

The present work considers (4+1)-dimensional spatially homogeneous vacuum cosmological models. Exact solutions -- some already existing in the literature, and others believed to be new -- are exhibited. Some of them are the most general for the corresponding Lie group with which each homogeneous slice is endowed, and some others are quite general. The characterization ``general'' is given based on the counting of the essential constants, the line-element of each model must contain; indeed, this is the basic contribution of the work. We give two different ways of calculating the number of essential constants for the simply transitive spatially homogeneous (4+1)-dimensional models. The first uses the initial value theorem; the second uses, through Peano's theorem, the so-called time-dependent automorphism inducing diffeomorphismsComment: 26 Pages, 2 Tables, latex2

Transnational regulation of temporary agency work compromised partnership between Private Employment Agencies and Global Union Federations

This article critically assesses the potential for the international regulation of temporary agency work (TAW) through building partnership between the Global Union Federations (GUFs) and major Private Employment Agencies (PrEAs). Given the limits of existing national and international regulation of TAW, particularly in developing countries, and the current deadlock in dialogue through the International Labour Organization, the argument of this article is that Transnational Private Labour Regulation (TPLR) offers a unique opportunity to establish a basis for minimum standards for temporary agency workers. This article goes on to propose three potential TPLR frameworks that, although compromised, are transparent, fair and sufficiently elastic to accommodate the distributive and political risks associated with partnership. They also offer important gains, namely increasing the competitive advantage of the PrEAs involved, minimum standards for agency workers and ‘field enlarging’ strategies for the GUFs and their affiliates

Performance of a 500 watt Nd:GGG zigzag slab oscillator

Realization of practical multi-kilowatt Nd:garnet lasers will require the scale-up of crystal dimensions as well as more powerful pumping sources. A high average power zigzag slab crystal amplifier testing facility has been established at LLNL which employs two 100 kW{sub e} vortex stabilized arc lamps, cooled reflectors and a cooled, spectrally filtered, crystal slab mounting fixture. The operational characteristics of the first crystal laser to be tested in this setup, a Nd:GGG zigzag oscillator, are presented. A Nd:GGG crystal of dimensions 18 {times} 7 {times} 0.5 cm{sup 3}, doped at 2 {times} 10{sup 20} cm{sup {minus}3} Nd{sup 3+} atomic density, was pumped by up to 40 kW of filtered argon line emission. A small-signal single pass gain (losses excluded) of 1.09 was measured with a probe laser when the DC input to the lamps was 43 kW{sub e}. Our power supply was then modified to operate in a pulsed mode and provided one to three milliseconds pulses at 120 Hz. An average optical output power of 490 watts was obtained at a lamp input power of 93 kW{sub e} in an unoptimized resonator. The laser output power declined after a few tens of seconds since the slab tips were not properly cooled. A birdhouse specular lamp reflector and a contoured diffuse reflector were tested; in both cases the pump illuminated crystal surface was smaller than the total crystal face area. Fluorescence imaging of the zigzag amplifier's output aperture registered a smoother, more uniform pumping profile when the diffuse reflector was used. Uniformity of pumping results in decreased resonator loss and yields higher laser output power. Thermo-optic distortions observed in these preliminary tests are analyzed with the aid of computer simulations of the thermal fields, stresses, and surface displacements of our crystal slab. 3 refs., 12 figs