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 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. CTP # 2455October 1995 (minor revisions December 1995) astro-ph/9510041 *

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 < 0.11h −2 times the closure density of the universe.

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

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

We derive an expression for the luminosity distance in Friedman-Lemaître-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 ( m , ) = (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.