On the Possibility of Anisotropic Curvature in Cosmology

In addition to shear and vorticity a homogeneous background may also exhibit anisotropic curvature. Here a class of spacetimes is shown to exist where the anisotropy is solely of the latter type, and the shear-free condition is supported by a canonical, massless 2-form field. Such spacetimes possess a preferred direction in the sky and at the same time a CMB which is isotropic at the background level. A distortion of the luminosity distances is derived and used to test the model against the CMB and supernovae (using the Union catalog), and it is concluded that the latter exhibit a higher-than-expected dependence on angular position. It is shown that future surveys could detect a possible preferred direction by observing ~ 20 / (\Omega_{k0}^2) supernovae over the whole sky.Comment: Extended SNe analysis and corrected some CMB results. Text also extended and references added. 8 pages, 5 figure

Qualitative Analysis of Universes with Varying Alpha

Assuming a Friedmann universe which evolves with a power-law scale factor, $a=t^{n}$, we analyse the phase space of the system of equations that describes a time-varying fine structure 'constant', $\alpha$, in the Bekenstein-Sandvik-Barrow-Magueijo generalisation of general relativity. We have classified all the possible behaviours of $\alpha (t)$ in ever-expanding universes with different $n$ and find new exact solutions for $\alpha (t)$. We find the attractors points in the phase space for all $n$. In general, $\alpha$ will be a non-decreasing function of time that increases logarithmically in time during a period when the expansion is dust dominated ($n=2/3$), but becomes constant when $n>2/3$. This includes the case of negative-curvature domination ($n=1$). $\alpha$ also tends rapidly to a constant when the expansion scale factor increases exponentially. A general set of conditions is established for $\alpha$ to become asymptotically constant at late times in an expanding universe.Comment: 26 pages, 6 figure

Detecting a Lorentz-Violating Field in Cosmology

We consider cosmology in the Einstein-aether theory (the generally covariant theory of gravitation coupled to a dynamical timelike Lorentz-violating vector field) with a linear aether-Lagrangian. The 3+1 spacetime splitting approach is used to derive covariant and gauge invariant perturbation equations which are valid for a general class of Lagrangians. Restricting attention to the parameter space of these theories which is consistent with local gravity experiments, we show that there are tracking behaviors for the aether field, both in the background cosmology and at linear perturbation level. The primordial power-spectrum of scalar perturbations in this model is shown to be the same that predicted by standard general relativity. However, the power-spectrum of tensor perturbation is different from that in general relativity, but has a smaller amplitude and so cannot be detected at present. We also study the implications for late-time cosmology and find that the evolution of photon and neutrino anisotropic stresses can source the aether field perturbation during the radiation and matter dominated epochs, and as a result the CMB and matter power spectra are modified. However these effects are degenerate with respect to other cosmological parameters, such as neutrino masses and the bias parameter in the observed galaxy spectrum.Comment: 13 pages, 3 figures; modified version to appear in Physical Review

Calibration of Pasture Forage Mass to Plate Meter Compressed Height is a Second-order Response with a Zero Intercept

Discusses how plant canopy structure effects the calibration between plate meter compressed height (CHt) and pasture forage mas

Extended Gravity Theories and the Einstein-Hilbert Action

I discuss the relation between arbitrarily high-order theories of gravity and scalar-tensor gravity at the level of the field equations and the action. I show that $(2n+4)$-order gravity is dynamically equivalent to Brans-Dicke gravity with an interaction potential for the Brans-Dicke field and $n$ further scalar fields. This scalar-tensor action is then conformally equivalent to the Einstein-Hilbert action with $n+1$ scalar fields. This clarifies the nature and extent of the conformal equivalence between extended gravity theories and general relativity with many scalar fields.Comment: 12 pages, Plain Latex, SUSSEX-AST-93/7-

False Vacuum Inflation with a Quartic Potential

We consider a variant of Hybrid Inflation, where inflation is driven by two interacting scalar fields, one of which has a `Mexican hat' potential and the other a quartic potential. Given the appropriate initial conditions one of the fields can be trapped in a false vacuum state, supported by couplings to the other field. The energy of this vacuum can be used to drive inflation, which ends when the vacuum decays to one of its true minima. Depending on parameters, it is possible for inflation to proceed via two separate epochs, with the potential temporarily steepening sufficiently to suspend inflation. We use numerical simulations to analyse the possibilities, and emphasise the shortcomings of the slow-roll approximation for analysing this scenario. We also calculate the density perturbations produced, which can have a spectral index greater than one.Comment: 10 pages, RevTeX 3.0, no figure

Diagnostic Utility of Cerebral White Matter Integrity in Early Alzheimer's Disease

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Neuroscience on August 2010, available online: http://www.tandfonline.com/10.3109/00207454.2010.494788.We compared white matter integrity with brain atrophy in healthy controls and participants with very mild dementia (Clinical Dementia Rating 0 vs. 0.5) from the Brain Aging Project, a longitudinal study of aging and memory at the University of Kansas Medical Center. Structural magnetic resonance imaging and diffusion tensor imaging (DTI) including fractional anisotropy and mean diffusivity were performed on 27 patients with very mild dementia (Clinical Dementia Rating = 0.5) of the Alzheimer's type (DAT), and 32 cognitively normal subjects. Patient groups were compared across 6 volumetric measures and 14 DTI regions of interest. Very mildly demented patients showed expected disease-related patterns of brain atrophy with reductions in whole-brain and hippocampal volumes most prominent. DTI indices of white matter integrity were mixed. Right parahippocampus showed significant but small disease-related reductions in fractional anisotropy. Right parahippocampus and left internal capsule showed greater mean diffusivity in early DAT compared with controls. A series of discriminant analyses demonstrated that gray matter atrophy was a significantly better predictor of dementia status than were DTI indices. Brain atrophy was most strongly related to very mild DAT. Modest disease-related white matter anomalies were present in temporal cortex, and deep white matter had limited discriminatory diagnostic power, probably because of the very mild stage of disease in these participants