Beyond the Thin Lens Approximation

We obtain analytic formulae for the null geodesics of Friedmann-Lema\^{\i}tre-Robertson-Walker spacetimes with scalar perturbations in the longitudinal gauge. From these we provide a rigorous derivation of the cosmological lens equation, and obtain an expression for the magnification of a bundle of light rays without restriction to static or thin lens scenarios. We show how the usual magnification matrix naturally emerges in the appropriate limits.Comment: 37 pages plus 3 appended figures, plain TeX. Submitted to Ap

Quasar Proper Motions and Low-Frequency Gravitational Waves

We report observational upper limits on the mass-energy of the cosmological gravitational-wave background, from limits on proper motions of quasars. Gravitational waves with periods longer than the time span of observations produce a simple pattern of apparent proper motions over the sky, composed primarily of second-order transverse vector spherical harmonics. A fit of such harmonics to measured motions yields a 95%-confidence limit on the mass-energy of gravitational waves with frequencies <2e-9 Hz, of <0.11/h*h times the closure density of the universe.Comment: 15 pages, 1 figure. Also available at http://charm.physics.ucsb.edu:80/people/cgwinn/cgwinn_group/index.htm

Null Geodesics in Perturbed Spacetimes

We present a generalization and refinement of the Sachs-Wolfe technique which unifies many of the approaches taken to date and clarifies both the physical and the mathematical character of the method. We illustrate the formalism with a calculation of the behavior of light passing a moving lens on a Minkowski background.Comment: 24 page

A Texture Bestiary

Textures are topologically nontrivial field configurations which can exist in a field theory in which a global symmetry group $G$ is broken to a subgroup $H$, if the third homotopy group \p3 of $G/H$ is nontrivial. We compute this group for a variety of choices of $G$ and $H$, revealing what symmetry breaking patterns can lead to texture. We also comment on the construction of texture configurations in the different models.Comment: 34 pages, plain Tex. (Minor corrections to an old paper.

Gravitational Radiation and Very Long Baseline Interferometry

Gravitational waves affect the observed direction of light from distant sources. At telescopes, this change in direction appears as periodic variations in the apparent positions of these sources on the sky; that is, as proper motion. A wave of a given phase, traveling in a given direction, produces a characteristic pattern of proper motions over the sky. Comparison of observed proper motions with this pattern serves to test for the presence of gravitational waves. A stochastic background of waves induces apparent proper motions with specific statistical properties, and so, may also be sought. In this paper we consider the effects of a cosmological background of gravitational radiation on astrometric observations. We derive an equation for the time delay measured by two antennae observing the same source in an Einstein-de Sitter spacetime containing gravitational radiation. We also show how to obtain similar expressions for curved Friedmann-Robertson-Walker spacetimes.Comment: 31 pages plus 3 separate figures, plain TeX, submitted to Ap

The Collapse of Exotic Textures

The ordering of scalar fields after a phase transition in which a group $G$ of global symmetries is spontaneously broken to a subgroup $H$ provides a possible explanation for the origin of structure in the universe, as well as leading to observable effects in condensed matter systems. The field dynamics can depend in principle on the geometry and topology of the vacuum manifold G/H; for example, texture configurations which collapse and unwind will exist if the third homotopy group $\pi_3(G/H)$ is nontrivial. We numerically simulate the evolution of texture-like configurations in a number of different models, in order to determine the extent to which the geometry and topology of the vacuum manifold influences the field evolution. We find that the dynamics is affected by whether or not the theory supports strings or monopoles [characterized by $\pi_1(G/H)$ and $\pi_2(G/H)$, respectively]. In some of the theories studied, configurations with initially spherically symmetric energy densities are unstable to nonspherical collapse; these theories are also found to nucleate defects during the collapse. Models that do not support monopoles or strings behave similarly to each other, regardless of the specific vacuum manifold.Comment: 28 pages plus 10 figures. Additional figures and mpeg movies accessible from http://itp.ucsb.edu/~carroll/textures.htm

Higher-Order Gravitational Perturbations of the Cosmic Microwave Background

We study the behavior of light rays in perturbed Robertson-Walker cosmologies, calculating the redshift between an observer and the surface of last scattering to second order in the metric perturbation. At first order we recover the classic results of Sachs and Wolfe, and at second order we delineate the various new effects which appear; there is no {\it a priori} guarantee that these effects are significantly smaller than those at first order, since there are large length scales in the problem which could lead to sizable prefactors. We find that second order terms of potential observational interest may be interpreted as transverse and longitudinal lensing by foreground density perturbations, and a correction to the integrated Sachs-Wolfe effect.Comment: 21 pages, one figure; minor corrections, new reference