Isotropic singularities in shear-free perfect fluid cosmologies

We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.Comment: 21 pages, 1 figur

Quiescent cosmology and the final state of the universe

It has long been a primary objective of cosmology to understand the apparent isotropy in our universe and to provide a mathematical formulation for its evolution. A school of thought for its explanation is quiescent cosmology, which already possesses a mathematical framework, namely the definition of an Isotropic Singularity, but only for the initial state of the universe. A complementary framework is necessary in order to also describe possible final states of the universe. Our new definitions of an Anisotropic Future Endless Universe and an Anisotropic Future Singularity, whose structure and properties differ significantly from those of the Isotropic Singularity, offer a promising realisation for this framework. The combination of the three definitions together may then provide the first complete formalisation of the quiescent cosmology concept.Comment: 7 pages, 3 figures, essay receiving honorable mention in the 2007 Gravity Research Foundation Essay award

A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary

We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use the Abstract Boundary to describe the structure of the `edge' of our manifold without resorting to structures external to the manifold itself. This is particularly important in the study of singularities within General Relativity where singularities lie on this `edge'. The ability to talk about the same objects, e.g., singularities, via different structures provides alternative routes for investigation which can be invaluable in the pursuit of physically motivated problems where certain types of information are unavailable or difficult to use.Comment: 23 page

Influences of lateral preference and personality on behaviour towards a manual sorting task

Differences in task behaviour between left- and right-handers and left- and right-eared individuals have been reported (e.g. Jackson, 2008 and Wright et al., 2004) with left-handers taking longer to begin a task and right-eared individuals having a more disinhibited approach. Personality measurements are also important when examining approach behaviour. Jackson (2008) reported that those with higher neuroticism levels and a right-ear preference react faster to tasks. The current study investigated the effects of lateral preference and personality on behaviour towards a manual sorting task. Eighty-five participants completed laterality and personality scales and a card-sorting task. Degree of hand preference was found to influence behaviour towards the task with strong left-handers taking longer to begin. Those with a left congruent lateral preference (left-hand, left-ear) took significantly longer to begin the task than those with a right congruent preference. Neither neuroticism nor extraversion influenced task approach. We concluded that hand preference, and more specifically a strong left-hand preference is a good predictor of a longer initiation time on a manual task. Ear preference on its own does not predict initiation time

The Cost of Complexity in Federal Student Aid: Lessons from Optimal Tax Theory and Behavioral Economics

The federal system for distributing student financial aid rivals the tax code in its complexity. Both have been a source of frustration and a focus of reform efforts for decades, yet the complexity of the student aid system has received comparatively little attention from economists. We describe the complexity of the aid system, and apply lessons from optimal tax theory and behavioral economics to show that complexity is a serious obstacle to both efficiency and equity in the distribution of student aid. We show that complexity disproportionately burdens those with the least ability to pay and undermines redistributive goals. We use detailed data from federal student aid applications to show that a radically simplified aid process can reproduce the current distribution of aid using a fraction of the information now collected.