We derive an expression for the luminosity distance in Friedman-Lemaitre-Robertson-Walker space-times affected by scalar perturbations. Our expression is complete to linear order and is expressed entirely in terms of standard cosmological parameters and observational quantities. We illustrate the result by calculating the rms scatter in the usual luminosity distance in flat (Omega(m), Omega(Lambda)) = (1.0, 0.0) and (0.3, 0.7) cosmologies. In both cases the scatter is appreciable at high redshifts, and rises above 11 per cent at z= 2, where it may be the dominant noise term in the Hubble diagram based on Type Ia supernovae.

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 ν < 2 × 10-9 Hz, of less than 0.11 h-2 times the closure density of the universe.

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.

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.

We obtain analytic formulae for the null geodesics of Friedmann-Lema\^{\i}tre-Robertson-Walker spacetimes with scalar perturbations in the longitudinal gauge. We use these to provide a rigorous derivation of the cosmological lens equation. We obtain an expression for the magnification of a bundle of light rays in these spacetimes without restriction to static or thin lens scenarios. We show how the usual magnification matrix naturally emerges in the appropriate limits.

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 pi3 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.

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

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 3 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.