Eccentric inflation and WMAP

For uniform arrangements of magnetic fields, strings, or domain walls (together with the cosmological constant and non-relativistic matter), exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal expansion. We argue the results can be used to explain some features in the WMAP data. The magnetic field case is the easiest to motivate and has the highest possibility of yielding reliable constraints on observational cosmology.Comment: 5 pages, 1 figur

Construction of multi-instantons in eight dimensions

We consider an eight-dimensional local octonionic theory with the seven-sphere playing the role of the gauge group. Duality conditions for two- and four-forms in eight dimensions are related. Dual fields--octonionic instantons--solve an 8D generalization of the Yang-Mills equation. Modifying the ADHM construction of 4D instantons, we find general $k$-instanton 8D solutions which depends on $16k-7$ effective parameters

Decomposition of geometric perturbations

For an infinitesimal deformation of a Riemannian manifold, we prove that the scalar, vector, and tensor modes in decompositions of perturbations of the metric tensor, the scalar curvature, the Ricci tensor, and the Einstein tensor decouple if and only if the manifold is Einstein. Four-dimensional space-time satisfying the condition of the theorem is homogeneous and isotropic. Cosmological applications are discussed.Comment: 7 page

A practical approach to cosmological perturbations in modified gravity

The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations, departures from the growth in the LCDM model can be quantified in terms of two functions of time and Fourier number k. We argue that in local theories of gravity, in the quasi-static approximation, these functions must be ratios of polynomials in k, with the numerator of one function being equal to the denominator of the other. Moreover, the polynomials are even and of second degree in practically all viable models considered today. This means that, without significant loss of generality, one can use data to constraint only five functions of a single variable, instead of two functions of two variables. Furthermore, since the five functions are expected to be slowly varying, one can fit them to data in a non-parametric way with the aid of an explicit smoothness prior. We discuss practical application of this parametrization to forecasts and fits.Comment: 9 pages, v2: matching the published versio

The Transverse Quark Distribution and Proton Electromagnetic Form Factors in Skew Distribution Formalism

Skew density matrices can be diagonalized to yield probability interpretation. The power-counting prediction of perturbative QCD is found consistent with recent CEBAF data on $F_2(Q^2)/F_1(Q^2)$Comment: 4 pages, Presented May 23, 2000 by John Ralston. Published in the Proceedings of the 7th International Conference on Intersections of Particle and Nuclear Physics, (May 22-28, 2000 Quebec City), Edited by Z. Parseh and W. Marciano, (AIP Conference Proceedings Number 549.

Electromagnetic Form Factors and the Localization of Quark Orbital Angular Momentum in the Proton

A new picture is given of generalized parton distributions probed in experiments in which the probe scale $Q^{2}$ and the momentum transfer \DD^{2} are well separated. Application of this picture to the $Q^{2}$ dependence of the form factors $F_{1}, F_{2}$ shows that gauge invariant quark orbital angular momentum can be measured and indeed {\it localized} in the transverse profile of the proton. A previous prediction that $\sqrt{Q^{2}}F_{2}(Q^{2})/F_{1}(Q^{2}) \sim const.$ is generalized to GPD language. This prediction appears to have been confirmed by recent CEBAF data.Comment: 6 pages, 1 figure. To appear in DIS 2001, 9th International Workshop on Deep Inelastic Scattering, Bologna, 27 April - 1 May, 200